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A199710
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Expansion of (1+x-14*x^2+13*x^3)/(1-28*x^2+169*x^4).
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3
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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).
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MATHEMATICA
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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 *)
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PROG
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(PARI) Vec((1+x-14*x^2+13*x^3)/(1-28*x^2+169*x^4)+O(x^25))
(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]];
(Maxima) makelist(expand(((1+3*sqrt(3))^n+(1-3*sqrt(3))^n)/(2*2^floor(n/2))), n, 0, 24);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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