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

%I

%S 1,1,14,41,223,979,3878,20483,70897,408073,1329734,7964417,25250959,

%T 154039339,482301806,2967115019,9237038497,57046572241,177128072702,

%U 1095861584537,3398526529663,21043253658307,65224098543926,404010494645843,1251923775716881

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

%H Bruno Berselli, <a href="/A199710/b199710.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,28,0,-169).

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

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

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

%t LinearRecurrence[{0, 28, 0, -169}, {1, 1, 14, 41}, 25]

%t CoefficientList[Series[(1+x-14x^2+13x^3)/(1-28x^2+169x^4),{x,0,30}],x] (* _Harvey P. Dale_, Nov 08 2017 *)

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

%o (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]];

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

%Y Cf. A002531, A083332.

%K nonn,easy

%O 0,3

%A _Bruno Berselli_, Nov 10 2011

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)