login
A246936
Number of partitions of n into 4 sorts of parts.
6
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 08 2014
STATUS
approved