A218569 Number of partitions p of n such that max(p)-min(p) = 6.

1, 1, 3, 3, 7, 8, 14, 18, 27, 33, 49, 59, 81, 100, 131, 158, 205, 243, 306, 365, 448, 527, 642, 748, 896, 1042, 1231, 1418, 1667, 1906, 2215, 2527, 2909, 3298, 3781, 4260, 4847, 5446, 6158, 6886, 7756, 8633, 9669, 10738, 11970, 13239, 14713, 16212, 17943

Offset: 8

Author

Alois P. Heinz, Nov 02 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..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

Table[Count[IntegerPartitions[n],?(First[#]-Last[#]==6&)],{n,8,60}] (* _Harvey P. Dale, Feb 09 2015 *)

Formula

G.f.: Sum_{k>0} x^(2*k+6)/Product_{j=0..6} (1-x^(k+j)).

a(n) = A097364(n,6) = A116685(n,6) = A194621(n,6) - A194621(n,5) = A218508(n) - A218507(n).