A246936 Number of partitions of n into 4 sorts of parts.

1, 4, 20, 84, 356, 1444, 5876, 23604, 94852, 379908, 1521492, 6088148, 24360548, 97451492, 389838708, 1559394356, 6237711300, 24951007620, 99804576340, 399218968084, 1596878076132, 6387515000292, 25550068873908, 102200286367156, 408801181153476

Offset

0,2

Links

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

Formula

G.f.: Product_{i>=1} 1/(1-4*x^i).

a(n) ~ c * 4^n, where c = Product_{k>=1} 1/(1-1/4^k) = A065446 * A132020 = 1.4523536424495970158347... . - Vaclav Kotesovec, Mar 19 2015

G.f.: Sum_{i>=0} 4^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1) +`if`(i>n, 0, 4*b(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

(O[x]^20 - 3/QPochhammer[4, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1]+If[i>n, 0, 4 b[n-i, i]]]];
a[n_] := b[n, n];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A246935.

Sequence in context: A155721 A084240 A080674 * A110154 A158608 A282084

Adjacent sequences: A246933 A246934 A246935 * A246937 A246938 A246939

Keyword

nonn

Author

Alois P. Heinz, Sep 08 2014

Status

approved