A184645 Number of partitions of n having no parts with multiplicity 10.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 56, 76, 100, 133, 174, 227, 293, 378, 482, 614, 777, 980, 1229, 1538, 1913, 2375, 2936, 3619, 4445, 5447, 6650, 8102, 9844, 11929, 14421, 17397, 20934, 25141, 30130, 36035, 43014, 51253, 60952, 72367, 85771, 101488

Offset

0,3

Links

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

Formula

a(n) = A000041(n) - A183567(n).

a(n) = A183568(n,0) - A183568(n,10).

G.f.: Product_{j>0} (1-x^(10*j)+x^(11*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=10, [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 == 10, {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, A183567, A183568, A007690, A116645, A118807, A184639, A184640, A184641, A184642, A184643, A184644.

Sequence in context: A036009 A261776 A027344 * A053691 A242696 A218510

Adjacent sequences: A184642 A184643 A184644 * A184646 A184647 A184648

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2011

Status

approved