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A100504
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a(n) = (4*n^3 + 6*n^2 + 8*n + 6)/3.
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3
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2, 8, 26, 64, 130, 232, 378, 576, 834, 1160, 1562, 2048, 2626, 3304, 4090, 4992, 6018, 7176, 8474, 9920, 11522, 13288, 15226, 17344, 19650, 22152, 24858, 27776, 30914, 34280, 37882, 41728, 45826, 50184, 54810, 59712, 64898, 70376, 76154, 82240
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: 2*(1+3*x^2)/(1-x)^4;
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
E.g.f.: (2/3)*(3 + 9*x + 9*x^2 + 2*x^3)*exp(x). (End)
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MATHEMATICA
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CoefficientList[Series[2*(1+3x^2)/((1-x)^4), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {2, 8, 26, 64}, 40] (* Harvey P. Dale, Dec 27 2015 *)
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PROG
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(Magma) I:=[2, 8, 26, 64]; [n le 4 select I[n] else 4*Self(n-1) -6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 26 2012
(SageMath) [2 + 2*n*(2*n^2+3*n+4)/3 for n in range(41)] # G. C. Greubel, Apr 03 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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EXTENSIONS
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STATUS
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approved
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