A204461 Number of n-element subsets that can be chosen from {1,2,...,5*n} having element sum n*(5*n+1)/2.

1, 1, 5, 25, 177, 1394, 11963, 108108, 1016737, 9853759, 97809616, 989878326, 10180316707, 106124695130, 1119148085092, 11920389375524, 128077285062639, 1386689101261013, 15115933170815361, 165776800325379769, 1828006462946421194, 20256667860779557632

Offset

0,3

Comments

a(n) is the number of partitions of n*(5*n+1)/2 into n distinct parts <=5*n.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Example

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

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*(5*n+1)/2, 5*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(5n+1)/2, 5n, n];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Row n=5 of A204459.

Sequence in context: A137383 A049035 A047897 * A121144 A096684 A265184

Adjacent sequences: A204458 A204459 A204460 * A204462 A204463 A204464

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2012

Status

approved