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A263615
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Partial sums of A263614 starting at n=2.
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2
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2, 4, 8, 12, 20, 28, 44, 59, 89, 115, 167, 209, 293, 357, 485, 578, 764, 894, 1154, 1330, 1682, 1914, 2378, 2677, 3275, 3653, 4409, 4879, 5819, 6395, 7547, 8244, 9638, 10472, 12140, 13128, 15104, 16264, 18584, 19935, 22637, 24199, 27323, 29117, 32705, 34753, 38849, 41174, 45824, 48450
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OFFSET
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2,1
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LINKS
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G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]
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FORMULA
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a(n) = (2*n*(3*n^3-14*n^2+147*n+272)+(4*n^3-30*n^2+128*n-27)*(-1)^n-741)/768.
G.f.: x^2*(x^7-4*x^5-4*x^4+4*x^3+4*x^2-2*x-2) / ((x-1)^5*(x+1)^4).
(End)
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MATHEMATICA
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LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {2, 4, 8, 12, 20, 28, 44, 59, 89}, 50] (* Harvey P. Dale, Feb 07 2024 *)
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PROG
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(PARI) a(n) = (2*n*(3*n^3-14*n^2+147*n+272)+(4*n^3-30*n^2+128*n-27)*(-1)^n-741)/768 \\ Colin Barker, Oct 26 2015
(PARI) Vec(x^2*(x^7-4*x^5-4*x^4+4*x^3+4*x^2-2*x-2)/((x-1)^5*(x+1)^4) + O(x^100)) \\ Colin Barker, Oct 26 2015
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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