A322939 a(n) = [x^n] (4*x^2 + x - 1)/(4*x^3 + 3*x^2 + 2*x - 1).

1, 1, 1, 9, 25, 81, 273, 889, 2921, 9601, 31521, 103529, 340025, 1116721, 3667633, 12045529, 39560841, 129928801, 426722241, 1401474249, 4602830425, 15116972561, 49648333393, 163058906169, 535530702761, 1758831457601, 5776490648161, 18971598480169, 62307994735225

Offset: 0

Author

Peter Luschny, Jan 06 2019

Keywords

• nonn

Crossrefs

Cf. A322940.

Programs

Maple

gf := (4*x^2 + x - 1)/(4*x^3 + 3*x^2 + 2*x - 1): ser := series(gf, x, 22):
seq(coeff(ser, x, n), n = 0..20);
a := proc(n) option remember;
`if`(n < 3, [1, 1, 1][n+1], 4*a(n-3) + 3*a(n-2) + 2*a(n-1)) end:

Formula

a(n) = 4*a(n-3) + 3*a(n-2) + 2*a(n-1) for n >= 3.