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

Author

Alois P. Heinz, Nov 02 2012

Keywords

• nonn

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

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 *)

Formula

G.f.: Sum_{k>0} x^(2*k+8)/Product_{j=0..8} (1-x^(k+j)).

a(n) = A097364(n,8) = A116685(n,8) = A194621(n,8) - A194621(n,7) = A218510(n) - A218509(n).