A204465 Number of n-element subsets that can be chosen from {1,2,...,9*n} having element sum n*(9*n+1)/2.

1, 1, 9, 85, 1143, 17053, 276373, 4721127, 83916031, 1537408202, 28851490163, 552095787772, 10736758952835, 211657839534446, 4221164530621965, 85031286025167082, 1727896040082882283, 35382865902724442331, 729502230296220422918, 15132164184348997874504

Offset

0,3

Comments

a(n) is the number of partitions of n*(9*n+1)/2 into n distinct parts <=9*n.

Links

Table of n, a(n) for n=0..19.

Example

a(2) = 9 because there are 9 2-element subsets that can be chosen from {1,2,...,18} having element sum 19: {1,18}, {2,17}, {3,16}, {4,15}, {5,14}, {6,13}, {7,12}, {8,11}, {9,10}.

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*(9*n+1)/2, 9*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(9n+1)/2, 9n, n];
a /@ Range[0, 10] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Row n=9 of A204459.

Sequence in context: A196955 A361283 A029711 * A276242 A015581 A152261

Adjacent sequences: A204462 A204463 A204464 * A204466 A204467 A204468

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2012

Status

approved