A218572 Number of partitions p of n such that max(p)-min(p) = 9.

1, 1, 3, 3, 7, 8, 14, 18, 28, 35, 53, 66, 92, 117, 157, 196, 259, 319, 411, 507, 638, 777, 970, 1171, 1438, 1728, 2098, 2501, 3012, 3563, 4251, 5008, 5923, 6931, 8152, 9486, 11078, 12835, 14900, 17177, 19844, 22768, 26169, 29916, 34219, 38954, 44387, 50338

Offset: 11

Author

Alois P. Heinz, Nov 02 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 11..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 = 11; 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[9], offset] (* Jean-François Alcover, Sep 11 2017, after Alois P. Heinz *)

Formula

G.f.: Sum_{k>0} x^(2*k+9)/Product_{j=0..9} (1-x^(k+j)).

a(n) = A097364(n,9) = A116685(n,9) = A194621(n,9) - A194621(n,8) = A218511(n) - A218510(n).