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) = 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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 08 2014
STATUS
editing