A220946 Expansion of (1+2*x+2*x^2-x^3)/((1-x)*(1+x)*(1-3x^2)).

1, 2, 6, 7, 21, 22, 66, 67, 201, 202, 606, 607, 1821, 1822, 5466, 5467, 16401, 16402, 49206, 49207, 147621, 147622, 442866, 442867, 1328601, 1328602, 3985806, 3985807, 11957421, 11957422, 35872266, 35872267, 107616801, 107616802, 322850406, 322850407

Offset: 0

Author

Philippe Deléham, Apr 14 2013

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A060816, A134931.

Programs

Mathematica

LinearRecurrence[{0, 4, 0, -3}, {1, 2, 6, 7}, 40] (* T. D. Noe, Apr 17 2013 *)

Formula

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

a(2n) = A134931(n), a(2n+1) = A060816(n+1).

a(n) = 4*a(n-2) - 3*a(n-4) with a(0)=1, a(1)=2, a(2)=6, a(3)=7.