A220944 Expansion of (1+3*x+5*x^2-x^3)/((1-x^2)*(1-3*x^2)).

1, 3, 9, 11, 33, 35, 105, 107, 321, 323, 969, 971, 2913, 2915, 8745, 8747, 26241, 26243, 78729, 78731, 236193, 236195, 708585, 708587, 2125761, 2125763, 6377289, 6377291, 19131873, 19131875, 57395625, 57395627, 172186881, 172186883, 516560649, 516560651

Offset: 0

Author

Philippe Deléham, Apr 13 2013

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -3).

Crossrefs

Cf. A036543, A171498.

Programs

Mathematica

LinearRecurrence[{0, 4, 0, -3}, {1, 3, 9, 11}, 40] (* T. D. Noe, Apr 17 2013 *)

Formula

a(n) = a(n-1)+2 if n odd.

a(n) = a(n-1)*3 if n even.

a(2n) = 4*3^n-3 = A036543(n), a(2n+1) = 4*3^n-1 = A171498(n).

a(n) = 4*a(n-2) - 3*a(n-4) with a(0)=1, a(1)=3, a(2)=9, a(3)=11.