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A232494
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If n mod 2 = 0 then 2^(n-1)*(3^n+3*3^(n/2)-2) otherwise 2^(n-1)*(3^n+5*3^((n-1)/2)-2).
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0
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1, 6, 32, 160, 848, 4576, 25856, 148480, 870656, 5142016, 30605312, 182640640, 1092866048, 6545268736, 39235813376, 235271618560, 1411199860736, 8465479499776, 50787717742592, 304705668382720, 1828172095029248, 10968784904912896, 65811966429495296, 394868826560266240, 2369204043294703616
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: ( -1+2*x+16*x^2 ) / ( (6*x-1)*(2*x-1)*(12*x^2-1) ). - R. J. Mathar, Dec 04 2013
a(n) = 2^(n-2) * (2 * 3^n - 4 + 3^((n-1)/2)(5 + 3*sqrt(3) + (-1)^n * (3*sqrt(3) - 5))). - Benedict W. J. Irwin, Sep 27 2016
E.g.f.: (1/12)*exp(-2*sqrt(3)*x)*(9 - 5*sqrt(3) + (9 + 5*sqrt(3))*exp(4*sqrt(3)*x) - 12*exp(2*(1 + sqrt(3))*x) + 6*exp(2*(3 + sqrt(3))*x)). - Stefano Spezia, Jan 09 2019
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MAPLE
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f:=proc(n)
if (n mod 2) = 0 then 2^(n-1)*(3^n+3*3^(n/2)-2) else
2^(n-1)*(3^n+5*3^((n-1)/2)-2) fi; end;
[seq(f(n), n=0..40)];
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MATHEMATICA
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Table[2^(n - 2) * (-4 + 2 3^n + 3^(n/2 - 1/2)(5 - 5(-1)^n + 3Sqrt[3] + 3(-1)^n Sqrt[3])), {n, 0, 20}] (* Benedict W. J. Irwin, Sep 27 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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