A360856 a(n) = [x^n](1/2)*(1 + (2*x + 1)/sqrt(1 - 8*x^2*(x + 1))).

1, 1, 2, 6, 16, 48, 140, 424, 1280, 3920, 12032, 37184, 115248, 358624, 1118784, 3499584, 10969344, 34450944, 108377984, 341465344, 1077300224, 3403006464, 10761447424, 34065967104, 107937899264, 342293526016, 1086339120128, 3450236511232, 10965437349888

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = (4*(2*n^2 - 11*n + 15)*a(n - 3) + 4*(2*n^2 - 9*n + 9)*a(n - 2) + 2*(n - 3)*a(n - 1)) / (n^2 - 3*n) for n >= 4.

Maple

gf := (1/2)*(1 + (2*x + 1)/sqrt(1 - 8*x^2*(x + 1)));
ser := series(gf, x, 30): seq(coeff(ser, x, n), n = 0..28);
# Recurrence:
a := proc(n) option remember; if n < 4 then return [1, 1, 2, 6][n + 1] fi:
(4*(2*n^2 - 11*n + 15)*a(n - 3) + 4*(2*n^2 - 9*n + 9)*a(n - 2) + 2*(n - 3)*a(n - 1)) / (n^2 - 3*n) end: seq(a(n), n = 0..28);

Crossrefs

Cf. A360571.

Sequence in context: A045694 A225178 A129772 * A046721 A230929 A367042

Adjacent sequences: A360853 A360854 A360855 * A360857 A360858 A360859

Keyword

nonn

Author

Peter Luschny, Feb 28 2023

Status

approved