A224692 Expansion of (1+5*x+7*x^2-x^3)/((1-2*x^2)*(1-x)*(1+x)).

1, 5, 10, 14, 28, 32, 64, 68, 136, 140, 280, 284, 568, 572, 1144, 1148, 2296, 2300, 4600, 4604, 9208, 9212, 18424, 18428, 36856, 36860, 73720, 73724, 147448, 147452, 294904, 294908, 589816, 589820, 1179640, 1179644, 2359288, 2359292, 4718584, 4718588, 9437176

Offset: 0

Author

Philippe Deléham, Apr 15 2013

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).

Crossrefs

Cf. A048491, A053209.

Programs

Mathematica

CoefficientList[Series[(1+5x+7x^2-x^3)/((1-2x^2)(1-x)(1+x)),{x,0,40}],x] (* or *) LinearRecurrence[{0,3,0,-2},{1,5,10,14},50] (* Harvey P. Dale, Sep 17 2016 *)

Formula

G.f.: (1+5*x+7*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)).

a(n) = a(n-1)+4 if n odd.

a(n) = a(n-1)*2 if n even.

a(2n) = 9*2^n - 8 = A048491(n).

a(2n+1) = 9*2^n - 4 = A053209(n+1).

a(n) = 3*a(n-2) - 2*a(n-4) with n>3, a(0)=1, a(1)=5, a(2)=10, a(3)=14.

a(n) = 9*2^floor(n/2)-2*(-1)^n-6. [Bruno Berselli, Apr 27 2013]