A218568 Number of partitions p of n such that max(p)-min(p) = 5.

1, 1, 3, 3, 7, 8, 14, 17, 26, 31, 45, 54, 73, 87, 114, 135, 171, 200, 249, 290, 352, 406, 487, 560, 660, 752, 879, 997, 1153, 1298, 1489, 1671, 1900, 2121, 2397, 2665, 2992, 3311, 3701, 4081, 4535, 4982, 5514, 6042, 6655, 7265, 7977, 8686, 9502, 10314, 11248

Offset: 7

Author

Alois P. Heinz, Nov 02 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..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],?(Max[#]-Min[#]==5&)],{n,7,60}] (* _Harvey P. Dale, Sep 25 2015 *)

Formula

G.f.: Sum_{k>0} x^(2*k+5)/Product_{j=0..5} (1-x^(k+j)).

a(n) = A097364(n,5) = A116685(n,5) = A194621(n,5) - A194621(n,4) = A218507(n) - A218506(n).