A204463 Number of n-element subsets that can be chosen from {1,2,...,7*n} having element sum n*(7*n+1)/2.

1, 1, 7, 50, 519, 5910, 73294, 957332, 13011585, 182262067, 2615047418, 38257201350, 568784501596, 8571868074560, 130687117401934, 2012485947249822, 31262279693472267, 489374243181858825, 7712880007117038531, 122301036027089010734, 1949904188227477978314

Offset: 0

Author

Alois P. Heinz, Jan 18 2012

Keywords

• nonn

Comments

a(n) is the number of partitions of n*(7*n+1)/2 into n distinct parts <=7*n.

Examples

			a(2) = 7 because there are 7 2-element subsets that can be chosen from {1,2,...,14} having element sum 15: {1,14}, {2,13}, {3,12}, {4,11}, {5,10}, {6,9}, {7,8}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..80

Crossrefs

Row n=7 of A204459.

Programs

Maple

b:= proc(n, i, t) option remember;
      `if`(it*(2*i-t+1)/2, 0,
      `if`(n=0, 1, b(n, i-1, t) +`if`(n b(n*(7*n+1)/2, 7*n, n):
seq(a(n), n=0..20);

Mathematica

b[n_, i_, t_] /; it(2i-t+1)/2 = 0; b[0, , ] = 1;
b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[nJean-François Alcover, Dec 07 2020, after Alois P. Heinz *)