A360971 Number of multisets of size n with elements from [n] whose element sum is larger than the product of all elements.

0, 0, 2, 4, 6, 8, 12, 14, 17, 20, 23, 26, 30, 33, 38, 41, 44, 47, 52, 55, 60, 63, 68, 71, 76, 78, 84, 89, 93, 97, 103, 106, 111, 115, 121, 124, 128, 131, 138, 142, 146, 151, 159, 162, 168, 171, 176, 181, 187, 190, 196, 201, 206, 210, 218, 221, 227, 232, 238

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Example

a(2) = 2: [1,1], [1,2].
a(3) = 4: [1,1,1], [1,1,2], [1,2,2], [1,1,3].
a(4) = 6: [1,1,1,1], [1,1,1,2], [1,1,2,2], [1,1,1,3], [1,1,2,3], [1,1,1,4].
a(8) = 17: [1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,2], [1,1,1,1,1,1,2,2], [1,1,1,1,1,2,2,2], [1,1,1,1,1,1,1,3], [1,1,1,1,1,1,2,3], [1,1,1,1,1,1,3,3], [1,1,1,1,1,1,1,4], [1,1,1,1,1,1,2,4], [1,1,1,1,1,1,3,4], [1,1,1,1,1,1,1,5], [1,1,1,1,1,1,2,5], [1,1,1,1,1,1,1,6], [1,1,1,1,1,1,2,6], [1,1,1,1,1,1,1,7], [1,1,1,1,1,1,2,7], [1,1,1,1,1,1,1,8].

Maple

b:= proc(n, i, s, p) `if`(s+n*i<=p, 0, `if`(n=0 or i=1, 1, g(n, i, s, p))) end:
g:= proc(n, i, s, p) option remember; add(b(n-1, j, s+j, p*j), j=1..i) end:
a:= n-> b(n$2, 0, 1):
seq(a(n), n=0..60);

Mathematica

b[n_, i_, s_, p_] := If[s + n*i <= p, 0, If[n == 0 || i == 1, 1, g[n, i, s, p]]];
g[n_, i_, s_, p_] := g[n, i, s, p] = Sum[b[n-1, j, s+j, p*j], {j, 1, i}];
a[n_] := b[n, n, 0, 1];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Dec 09 2023, after Alois P. Heinz *)

Crossrefs

Cf. A103586, A360538, A360563.

Sequence in context: A273131 A372224 A357371 * A249721 A010063 A260652

Adjacent sequences: A360968 A360969 A360970 * A360972 A360973 A360974

Keyword

nonn

Author

Alois P. Heinz, Feb 27 2023

Status

approved