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

0,3

Comments

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

Links

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

Example

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}.

Maple

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

Mathematica

b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;
b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[n<i, 0, b[n-i, i-1, t-1]];
a[n_] := b[n(7n+1)/2, 7n, n];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Row n=7 of A204459.

Sequence in context: A267243 A197570 A319884 * A041086 A197890 A320989

Adjacent sequences: A204460 A204461 A204462 * A204464 A204465 A204466

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2012

Status

approved