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A184643 Number of partitions of n having no parts with multiplicity 8. 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 (list; graph; refs; listen; history; text; internal format)
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: A261775 A036007 A027342 * A307547 A182804 A242695

Adjacent sequences:  A184640 A184641 A184642 * A184644 A184645 A184646

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 18 2011

STATUS

approved

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Last modified July 7 13:21 EDT 2022. Contains 355148 sequences. (Running on oeis4.)