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a(n) = (-3)^n*A168074A061891(n).

Cf. A168074A061891, A168076.

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(MAGMAMagma) I:=[1, -3, 36, -189]; [n le 4 select I[n] else -3*Self(n-1)-27*Self(n-3)-81*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 10 2016

OEIS Server: https://oeis.org/edit/global/2944

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a(n) = 2*(-3)^n*n + 3^n*(sin(Pi*n/3)/sqrt(3) + cos(Pi*n/3)). - Ilya Gutkovskiy, Jul 10 2016

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1, -3, 36, -189, 567, -2430, 9477, -28431, 104976, -373977, 1121931, -3897234, 13286025, -39858075, 133923132, -444816117, 1334448351, -4390765542, 14334558093, -43003674279, 139471376040, -449795187729, 1349385563187, -4330586226042, 13839047287569

CoefficientList[Series[(1 + 27 x^2 - 54 x^3) / ((1 + 3 x)^2 (1 - 3 x + 9 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 10 2016 *)

(MAGMA) I:=[1, -3, 36, -189]; [n le 4 select I[n] else -3*Self(n-1)-27*Self(n-3)-81*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 10 2016

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Cf. A168074, A168076.

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