%I #6 Jan 06 2019 11:25:07
%S 1,1,1,9,25,81,273,889,2921,9601,31521,103529,340025,1116721,3667633,
%T 12045529,39560841,129928801,426722241,1401474249,4602830425,
%U 15116972561,49648333393,163058906169,535530702761,1758831457601,5776490648161,18971598480169,62307994735225
%N a(n) = [x^n] (4*x^2 + x - 1)/(4*x^3 + 3*x^2 + 2*x - 1).
%F a(n) = 4*a(n-3) + 3*a(n-2) + 2*a(n-1) for n >= 3.
%p gf := (4*x^2 + x - 1)/(4*x^3 + 3*x^2 + 2*x - 1): ser := series(gf, x, 22):
%p seq(coeff(ser, x, n), n = 0..20);
%p a := proc(n) option remember;
%p `if`(n < 3, [1, 1, 1][n+1], 4*a(n-3) + 3*a(n-2) + 2*a(n-1)) end:
%Y Cf. A322940.
%K nonn
%O 0,4
%A _Peter Luschny_, Jan 06 2019