A184643 Number of partitions of n having no parts with multiplicity 8.

1, 1, 2, 3, 5, 7, 11, 15, 21, 30, 41, 55, 75, 99, 131, 172, 223, 288, 372, 474, 603, 764, 962, 1206, 1509, 1876, 2326, 2878, 3543, 4351, 5330, 6506, 7921, 9623, 11655, 14085, 16987, 20434, 24529, 29392, 35138, 41930, 49947, 59381, 70474, 83512, 98779

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A000041(n) - A183565(n).

a(n) = A183568(n,0) - A183568(n,8).

G.f.: Product_{j>0} (1-x^(8*j)+x^(9*j))/(1-x^j).

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0, 0],
      add((l->`if`(j=8, [l[1]$2], l))(b(n-i*j, i-1)), j=0..n/i)))
    end:
a:= n-> (l-> l[1]-l[2])(b(n, n)):
seq(a(n), n=0..50);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, If[j == 8, {l[[1]], l[[1]]}, l]][b[n - i*j, i - 1]], {j, 0, n/i}]]];
a[n_] := b[n, n][[1]] - b[n, n][[2]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)

Crossrefs

Cf. A000041, A183565, A183568, A007690, A116645, A118807, A184639, A184640, A184641, A184642, A184644, A184645.

Sequence in context: A036007 A027342 A363231 * A307547 A182804 A242695

Adjacent sequences: A184640 A184641 A184642 * A184644 A184645 A184646

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2011

Status

approved