A182803 Number of 8-core partitions of n.

1, 1, 2, 3, 5, 7, 11, 15, 14, 22, 26, 32, 37, 45, 47, 56, 75, 77, 89, 102, 111, 124, 142, 147, 167, 182, 196, 210, 242, 249, 288, 322, 299, 349, 382, 393, 423, 467, 453, 499, 570, 563, 602, 669, 649, 716, 772, 754, 843, 907, 884

Offset

0,3

Links

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

Formula

G.f.: Product_{i>=1} (1-x^(8*i))^8/(1-x^i).

Euler transform of period 8 sequence [1,1,1,1,1,1,1,-7, .. ].

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, 8), n=0..50);

Mathematica

A[n_, t_] := A[n, t] = 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, 8], {n, 0, 50}] (* Jean-François Alcover, May 21 2018, translated form Maple *)

Crossrefs

8th column of A175595.

Sequence in context: A350836 A094252 A209038 * A106532 A240556 A090693

Adjacent sequences: A182800 A182801 A182802 * A182804 A182805 A182806

Keyword

nonn

Author

Alois P. Heinz, Dec 03 2010

Status

approved