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A005491
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a(n) = n^3 + 3*n + 1.
(Formerly M3855)
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5
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1, 5, 15, 37, 77, 141, 235, 365, 537, 757, 1031, 1365, 1765, 2237, 2787, 3421, 4145, 4965, 5887, 6917, 8061, 9325, 10715, 12237, 13897, 15701, 17655, 19765, 22037, 24477, 27091, 29885, 32865, 36037, 39407, 42981, 46765, 50765, 54987, 59437, 64121, 69045
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(0)=1, a(1)=5, a(2)=15, a(3)=37, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Oct 01 2014
E.g.f.: (1 + 4*x + 3*x^2 + x^3)*exp(x).
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MAPLE
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MATHEMATICA
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Table[n^3 + 3 n + 1, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 5, 15, 37}, 50] (* Harvey P. Dale, Oct 01 2014 *)
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PROG
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(SageMath) [(n+1)^3 -3*n^2 for n in range(51)] # G. C. Greubel, Dec 01 2022
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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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