A199710 Expansion of (1+x-14*x^2+13*x^3)/(1-28*x^2+169*x^4).

1, 1, 14, 41, 223, 979, 3878, 20483, 70897, 408073, 1329734, 7964417, 25250959, 154039339, 482301806, 2967115019, 9237038497, 57046572241, 177128072702, 1095861584537, 3398526529663, 21043253658307, 65224098543926, 404010494645843, 1251923775716881

Offset: 0

Author

Bruno Berselli, Nov 10 2011

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,28,0,-169).

Crossrefs

Cf. A002531, A083332.

Programs

Magma

I:=[1,1,14,41]; [n le 4 select I[n] else 28*Self(n-2)-169*Self(n-4): n in [1..25]];

Mathematica

LinearRecurrence[{0, 28, 0, -169}, {1, 1, 14, 41}, 25]
CoefficientList[Series[(1+x-14x^2+13x^3)/(1-28x^2+169x^4),{x,0,30}],x] (* Harvey P. Dale, Nov 08 2017 *)

Maxima

makelist(expand(((1+3*sqrt(3))^n+(1-3*sqrt(3))^n)/(2*2^floor(n/2))),n,0,24);

PARI

Vec((1+x-14*x^2+13*x^3)/(1-28*x^2+169*x^4)+O(x^25))

Formula

G.f.: (1+x-14*x^2+13*x^3)/(1-28*x^2+169*x^4).

a(n) = ((1+3*sqrt(3))^n+(1-3*sqrt(3))^n)/(2*2^floor(n/2)).

a(n) = 28*a(n-2)-169*a(n-4).