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A051500
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a(n) = (3^n + 1)^2/4.
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3
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1, 4, 25, 196, 1681, 14884, 133225, 1196836, 10764961, 96864964, 871725625, 7845353476, 70607649841, 635467254244, 5719200505225, 51472790198116, 463255068736321, 4169295489486724, 37523659017960025, 337712929999378756, 3039416366507624401
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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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a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3) for n > 2.
G.f.: (1-9*x+12*x^2) / ((1-x)*(1-3*x)*(1-9*x)). (End)
E.g.f.: (1/4)*(exp(x) + 2*exp(3*x) + exp(9*x)). - G. C. Greubel, May 22 2023
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MATHEMATICA
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(3^Range[0, 20]+1)^2/4 (* or *) LinearRecurrence[{13, -39, 27}, {1, 4, 25}, 30] (* Harvey P. Dale, Nov 05 2016 *)
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PROG
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(PARI) Vec((1-9*x+12*x^2)/((1-x)*(1-3*x)*(1-9*x)) + O(x^30)) \\ Colin Barker, Feb 10 2016
(Python)
(Magma) [(3^n+1)^2/4: n in [0..40]]; // G. C. Greubel, May 22 2023
(SageMath) [((3^n+1)//2)^2 for n in range(41)] # G. C. Greubel, May 22 2023
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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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