A184644 Number of partitions of n having no parts with multiplicity 9.

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 42, 55, 76, 99, 133, 172, 227, 290, 376, 477, 612, 769, 975, 1217, 1528, 1895, 2359, 2907, 3592, 4400, 5403, 6584, 8034, 9742, 11823, 14272, 17234, 20713, 24897, 29803, 35674, 42542, 50719, 60272, 71592, 84794

Offset

0,3

Links

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

Formula

a(n) = A000041(n) - A183566(n).

a(n) = A183568(n,0) - A183568(n,9).

G.f.: Product_{j>0} (1-x^(9*j)+x^(10*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=9, [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 == 9, {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, A183566, A183568, A007690, A116645, A118807, A184639, A184640, A184641, A184642, A184643, A184645.

Sequence in context: A036008 A104502 A027343 * A209039 A182805 A309058

Adjacent sequences: A184641 A184642 A184643 * A184645 A184646 A184647

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2011

Status

approved