A238631 Number of partitions of 4^n into parts that are at most 4.

1, 5, 64, 2280, 123464, 7566280, 478968264, 30569959880, 1955134763464, 125107148059080, 8006513870533064, 512411390124519880, 32794241006913221064, 2098830017067059278280, 134325098574291643691464, 8596805948466686953550280, 550195574937260409780728264

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (85,-1428,5440,-4096).

Formula

a(n) = [x^(4^n)] Product_{j=1..4} 1/(1-x^j).

G.f.: -(2048*x^4+1460*x^3-1067*x^2+80*x-1) / ((1-x) *(1-4*x) *(1-4^2*x) *(1-4^3*x)).

a(n) = (128 + 9*2^(3+2*n) + 15*16^n + 64^n)/144 for n > 0. - Stefano Spezia, Oct 08 2022

Maple

gf:= -(2048*x^4+1460*x^3-1067*x^2+80*x-1)/((1-x)*(1-4*x)*(1-4^2*x)*(1-4^3*x)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Crossrefs

Row n=4 of A238016.

Sequence in context: A061684 A061698 A351020 * A220557 A266962 A126955

Adjacent sequences: A238628 A238629 A238630 * A238632 A238633 A238634

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 01 2014

Status

approved