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

%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