DATA FILES

  • Coefficients of Andrews spt-function
    spt(n) = the number of occurences of smallest parts in the partitions of n.
    For example,
    Partitions of 4  Number of smallest parts
    4                1
    3+1              1
    2+2              2
    2+1+1            2
    1+1+1+1          4
    
    spt(4)=1+1+2+2+4=10.
    FILES
    • sptcofs.txt
      Text file containing spt(n) for n=1 to n=10000.
      This file has 10000 lines one for each value of spt(n).
    • sptcofsmod2.txt
      Text file contains spt(n) mod 220 for n=1 to n=200000.
    • sptcofs.m
      This is a MAPLE m-file which contains the array sptcofs.
      EXAMPLE:
      > read "sptcofs.m":
      > sptcofs[5999];
         278941830700915838882974455560132543710354527039490199582717253860798628323895514520
      
      > ifactor(%,easy);
                                     3
                                  (2)   (5)  (13)  (71)  (151) _c77_1
      
      
  • Partition function
    p(n) = the number of partitions of n.
    For example, p(4)=5 since there are 5 partitions of 4:
    4
    3+1
    2+2
    2+1+1
    1+1+1+1
    

    FILES
    • ptncofs.txt
      Text file containing p(n) for n=1 to n=10000.
      This file has 10000 lines one for each value of p(n).
    • ptncofs.m
      This is a MAPLE m-file which contains the array ptncofs.
      EXAMPLE:
      > read "ptncofs.m":
      > ptncofs[5999];
      4595772182112790143084312200387343025849540044362698346833677237664902997364019500
      
      > ifactor(%,easy);
                                  2     3
                               (2)   (5)   (13)  (353) _c76_1
      
      
  • Overpartition function
    pb(n) = the number of overpartitions of n.
    An overpartition is partition in which the first occurence of a part may be overlined. For example, pb(3)=8 since there are 8 overpartitions of 3:
    3
    3*
    2+1
    2+1*
    2*+1
    2*+1*
    1+1+1
    1*+1+1
    
    (Overline parts are marked by *).
    FILES
    • optncofs.txt
      Text file containing pb(n) for n=1 to n=10000.
      This file has 10000 lines one for each value of pb(n).
    • optncofs.m
      This is a MAPLE m-file which contains the array optncofs.
      EXAMPLE:
      > read "optncofs.m":
      > optncofs[1996];
                    561516259751768382289813036527907885842788143179605073720
      
      > ifactor(%,easy);                
                                      3     7
                                   (2)   (3)   (5)  (17) _c51_1
      
      
      
  • The Fishburn Numbers
    The Fishburn numbers xi(n) are defined by the formal power series
                               oo                        
                              -----                     
                               \                        
                                )           n           
                               /     xi(n) q  = F(1 - q)
                              -----                     
                              n = 0                     
    where                                              
                                       oo              
                                      -----           
                                       \              
                                        )             
                              F(q) =   /     (q, q)
                                      -----        n   
                                      n = 0           
    
    See oeis.org/A022493.
    FILES
    • fishcofs.txt
      Text file containing xi(n) for n=0 to n=500.
      This file has 501 lines one for each value of xi(n).
    • fishcofs.m
      This is a MAPLE m-file which contains the array fishcofs.
      EXAMPLE:
      > read "fishcofs.m":
      > seq(fishcofs[j],j=0..10);
                   1, 1, 2, 5, 15, 53, 217, 1014, 5335, 31240, 201608
      > with(qseries):
      > FISHGEN:=add(fishcofs[j]*q^j,j=0..500):
      > findcong(FISHGEN,500);
                                        [3, 5, 5]
                                        [4, 5, 5]
                                        [6, 7, 7]
                                       [8, 11, 11]
                                       [9, 11, 11]
                                      [10, 11, 11]
                                      [16, 17, 17]
                                      [17, 19, 19]
                                      [18, 19, 19]
       {[3, 5, 5], [4, 5, 5], [6, 7, 7], [8, 11, 11], [9, 11, 11], [10, 11, 11], 
      
         [16, 17, 17], [17, 19, 19], [18, 19, 19]}
      > fishcofs[499];
      
      2041540377336862271213859295254324886316095045962006087397212630197321
      6025717828916626588734439711670536972609795466338165650933183461403319
      0452113737608168468298799543465301468790439285581649949999660559759105
      6267250511758690788082972807169630797468437738392196362846571961118461
      1111827535977816518064118759873205540133387049061210002985012204510408
      9447841281138878318929507815014245267285520076642495312622941418256248
      0031917329067116437918696480663779901357852971537787345898196183079574
      3701544571822746943268232936793665500223423234752765265592045581896014
      0743386635004919983674742353758663460385790293303237243610990472431040
      5586446225550445712036228117355203759955173562943438424444977900503949
      0718500531939165695922807647025462631159998831303002322738902757230487
      2477106472423187802665733314010676048603528715558875468277182551486367
      2390874860358557531726372555920101639600037677125936474504987391102775
      1270057751770476250307879150074788095126290562042061493659572033163311
      2789550393792974047528517110286306569109856375
      
      > evalf(log(%)/log(10));
                                       1025.309958
      
      
      > ifactor(fishcofs[499],easy);
                                     3                    
                              (3) (5)  (13) (503) _c1019_1
      

The url of this page is http://qseries.org/fgarvan/data/index.html.
Created by F.G. Garvan (fgarvan@math.ufl.edu) on Wednesday, June 24, 2009.
Last update made Wed May 15 22:32:41 EDT 2013.


MAIL fgarvan@math.ufl.edu