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If n = (1 mod 4) or n = (1 mod 4), then a(n) = 3*a(n-2); otherwise, a(n) = 3*a(n-2) + 2.
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G.f.: (3 1 + 3 2*x - + x^2 + 3 x^3 - 6 3*x^45) / ((1 - x - 2 )*(1 + x^2 + 2 x^3 )*(1 - 3 x^4 + 3 *x^52)). - Corrected by _Colin Barker_, Jan 21 2018
(PARI) Vec((1 + 2*x + x^2 + x^3 - 3*x^5) / ((1 - x)*(1 + x^2)*(1 - 3*x^2)) + O(x^40)) \\ Colin Barker, Jan 21 2018
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<a href="/index/Rec#order_0205">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,3,-3)
G.f.: (3 + 3 x - x^2 + 3 x^3 - 6 x^4)/(1 - x - 2 x^2 + 2 x^3 - 3 x^4 + 3 x^5.
3 x^5).
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3 x^5).