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A176889
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a(2*k-1)=1, a(2*k)=2*k^2 (definition by T. M. Apostol, see References).
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1
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1, 2, 1, 8, 1, 18, 1, 32, 1, 50, 1, 72, 1, 98, 1, 128, 1, 162, 1, 200, 1, 242, 1, 288, 1, 338, 1, 392, 1, 450, 1, 512, 1, 578, 1, 648, 1, 722, 1, 800, 1, 882, 1, 968, 1, 1058, 1, 1152, 1, 1250, 1, 1352, 1, 1458, 1, 1568, 1, 1682, 1, 1800, 1, 1922, 1, 2048, 1, 2178
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OFFSET
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1,2
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REFERENCES
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T. M. Apostol, Calculus, Volume 1, John Wiley & Sons, 1967 (2nd ed.), p. 378-379.
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LINKS
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FORMULA
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G.f.: x*(1 + 2*x - 2*x^2 + 2*x^3 + x^4)/(1-x^2)^3.
a(n) = a(-n) = 1+((-1)^n+1)*(n^2-2)/4.
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MATHEMATICA
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CoefficientList[Series[(1 + 2 x - 2 x^2 + 2 x^3 + x^4) / (1 - x^2)^3, {x, 0, 65}], x] (* Vincenzo Librandi, Aug 19 2013 *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 2, 1, 8, 1, 18}, 70] (* Harvey P. Dale, Jul 18 2024 *)
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PROG
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(Magma) &cat[[1, 2*n^2]: n in [1..33]];
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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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