A098581 Expansion of (1+2*x+4*x^2)/(1-x-8*x^4).

1, 3, 7, 7, 15, 39, 95, 151, 271, 583, 1343, 2551, 4719, 9383, 20127, 40535, 78287, 153351, 314367, 638647, 1264943, 2491751, 5006687, 10115863, 20235407, 40169415, 80222911, 161149815, 323033071, 644388391, 1286171679, 2575370199

Offset: 0

Author

Paul Barry, Sep 16 2004

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,8).

Crossrefs

Cf. A078467, A097334.

Programs

Magma

I:=[1,3,7,7]; [n le 4 select I[n] else Self(n-1) + 8*Self(n-4): n in [1..30]]; // G. C. Greubel, Feb 03 2018

Mathematica

CoefficientList[Series[(1+2x+4x^2)/(1-x-8x^4),{x,0,40}],x] (* or *) LinearRecurrence[{1,0,0,8},{1,3,7,7},40] (* Harvey P. Dale, Feb 04 2015 *)

PARI

x='x+O('x^30); Vec((1+2*x+4*x^2)/(1-x-8*x^4)) \\ G. C. Greubel, Feb 03 2018

Formula

a(n) = a(n-1) + 8*a(n-4).

a(n) = Sum_{k=0..n} binomial(n-k, floor(k/3)) * 2^k.