A204460 Number of 2*n-element subsets that can be chosen from {1,2,...,8*n} having element sum n*(8*n+1).

1, 4, 86, 3486, 178870, 10388788, 652694106, 43304881124, 2990752400778, 212997373622366, 15542763534960598, 1156764114321375362, 87507330113965391948, 6711208401368504338646, 520758394504342278328914, 40818243590325732399837872, 3227693268242421225516534768

Offset

0,2

Comments

a(n) is the number of partitions of n*(8*n+1) into 2*n distinct parts <=8*n.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

Example

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

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*(8*n+1), 8*n, 2*n):
seq(a(n), n=0..15);

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(8n+1), 8n, 2n];
a /@ Range[0, 15] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Bisection of row n=4 of A204459.

Sequence in context: A163279 A130268 A293318 * A162086 A116320 A220277

Adjacent sequences: A204457 A204458 A204459 * A204461 A204462 A204463

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2012

Status

approved