A218571 Number of partitions p of n such that max(p)-min(p) = 8.
1, 1, 3, 3, 7, 8, 14, 18, 28, 35, 52, 65, 90, 113, 152, 188, 246, 302, 387, 471, 591, 714, 884, 1059, 1292, 1538, 1857, 2193, 2621, 3077, 3646, 4254, 4999, 5801, 6772, 7815, 9062, 10409, 12002, 13719, 15733, 17909, 20438, 23169, 26318, 29722, 33623, 37833
Offset: 10
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 10..1000
- G. E. Andrews, M. Beck and N. Robbins, Partitions with fixed differences between largest and smallest parts, arXiv:1406.3374 [math.NT], 2014.
Programs
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Mathematica
terms = 48; offset = 10; max = terms + offset; s[k0_ /; k0 > 0] := Sum[x^(2*k + k0)/Product[ (1 - x^(k + j)), {j, 0, k0}], {k, 1, Ceiling[max/2]}] + O[x]^max // CoefficientList[#, x] &; Drop[s[8], offset] (* Jean-François Alcover, Sep 11 2017, after Alois P. Heinz *)