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A057769
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a(n) = 4*n^4 + 8*n^3 - 4*n - 1 = (2*n^2 - 1)*(2*n^2 + 4*n + 1).
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5
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-1, 7, 119, 527, 1519, 3479, 6887, 12319, 20447, 32039, 47959, 69167, 96719, 131767, 175559, 229439, 294847, 373319, 466487, 576079, 703919, 851927, 1022119, 1216607, 1437599, 1687399, 1968407, 2283119, 2634127, 3024119, 3455879, 3932287, 4456319, 5031047, 5659639, 6345359, 7091567
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OFFSET
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0,2
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COMMENTS
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It may be seen that the terms of the (signed) sequence consist of a subset of the odd squares minus two.
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REFERENCES
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Albert H. Beiler, Recreations in the theory of numbers, New York: Dover, 2nd ed., 1966, p. 106, table 53.
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LINKS
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FORMULA
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a(n) = 4*b(n)^2 - 4*b(n) - 1 where b(n) = n-th pronic number A002378(n).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=-1, a(1)=7, a(2)=119, a(3)=527, a(4)=1519. - Harvey P. Dale, Oct 20 2011
G.f.: (x*(x*((x-12)*x-74)-12)+1)/(x-1)^5. - Harvey P. Dale, Oct 20 2011
Sum_{n>=0} 1/a(n) = cot(Pi/sqrt(2))*Pi/(2*sqrt(2)). - Amiram Eldar, Jan 22 2024
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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Stuart M. Ellerstein (ellerstein(AT)aol.com), Nov 01 2000
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EXTENSIONS
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STATUS
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approved
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