A182805 Number of 10-core partitions of n.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 32, 46, 57, 71, 85, 106, 121, 147, 165, 190, 242, 267, 302, 350, 400, 443, 511, 565, 638, 715, 774, 852, 964, 1038, 1135, 1253, 1372, 1482, 1650, 1785, 1878, 2098, 2234, 2411, 2625, 2819, 2963, 3249, 3393, 3600, 4004, 4181

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{i>=1} (1-x^(10*i))^10/(1-x^i).

Euler transform of period 10 sequence [1,1,1,1,1,1,1,1,1,-9, .. ].

Maple

with(numtheory): A:= proc(n, t) option remember; local d, j; `if`(n=0, 1, add(add(`if`(t=0 or irem(d, t)=0, d-d*t, d), d=divisors(j)) *A(n-j, t), j=1..n)/n) end: seq(A(n, 10), n=0..50);

Mathematica

A[n_, t_] := A[n, t] = Module[{d, j}, If[n == 0, 1, Sum[Sum[If[t == 0 || Mod[d, t] == 0, d - d t, d], {d, Divisors[j]}] A[n - j, t], {j, 1, n}]/n]];
Table[A[n, 10], {n, 0, 50}] (* Jean-François Alcover, Dec 06 2020, after Alois P. Heinz *)

Crossrefs

10th column of A175595.

Cf. A033687, A045831, A053723, A081622, A053724, A182803, A182804.

Sequence in context: A027343 A184644 A209039 * A309058 A218509 A026815

Adjacent sequences: A182802 A182803 A182804 * A182806 A182807 A182808

Keyword

nonn

Author

Alois P. Heinz, Dec 03 2010

Status

approved