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A033595
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a(n) = (n^2-1)*(2*n^2-1).
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1
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1, 0, 21, 136, 465, 1176, 2485, 4656, 8001, 12880, 19701, 28920, 41041, 56616, 76245, 100576, 130305, 166176, 208981, 259560, 318801, 387640, 467061, 558096, 661825, 779376, 911925, 1060696, 1226961
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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G.f.: (1 -5*x +31*x^2 +21*x^3)/(1-x)^5. - R. J. Mathar, Feb 06 2017
E.g.f.: (1 - x + 11*x^2 + 12*x^3 + 2*x^4)*exp(x). - G. C. Greubel, Mar 05 2020
From Amiram Eldar, Mar 11 2022: (Start)
Sum_{n>=2} 1/a(n) = (Pi/sqrt(2))*cot(Pi/sqrt(2)) + 7/4.
Sum_{n>=2} (-1)^n/a(n) = (Pi/sqrt(2))*cosec(Pi/sqrt(2)) - 11/4. (End)
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MAPLE
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seq( (n^2 -1)*(2*n^2 -1), n=0..40); # G. C. Greubel, Mar 05 2020
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MATHEMATICA
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Table[(n^2 -1)*(2*n^2 -1), {n, 0, 40}] (* G. C. Greubel, Mar 05 2020 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 0, 21, 136, 465}, 40] (* Harvey P. Dale, Aug 24 2020 *)
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PROG
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(PARI) vector(41, n, my(m=n-1); (m^2 -1)*(2*m^2 -1)) \\ G. C. Greubel, Mar 05 2020
(Magma) [(n^2 -1)*(2*n^2 -1): n in [0..40]]; // G. C. Greubel, Mar 05 2020
(Sage) [(n^2 -1)*(2*n^2 -1) for n in (0..40)] # G. C. Greubel, Mar 05 2020
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CROSSREFS
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Sequence in context: A264554 A125331 A126489 * A220388 A220151 A337899
Adjacent sequences: A033592 A033593 A033594 * A033596 A033597 A033598
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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