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A139757
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a(n) = (n+1)*(2n+1)^2.
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4
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1, 18, 75, 196, 405, 726, 1183, 1800, 2601, 3610, 4851, 6348, 8125, 10206, 12615, 15376, 18513, 22050, 26011, 30420, 35301, 40678, 46575, 53016, 60025, 67626, 75843, 84700, 94221, 104430, 115351, 127008, 139425, 152626, 166635, 181476
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OFFSET
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0,2
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COMMENTS
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Also the detour index of the (n+1)-antiprism graph and (n+1)-cocktail party graphs for n>=2. - Eric W. Weisstein, Jul 15 2011 and Dec 20 2017
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LINKS
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FORMULA
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a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4); G.f.: (1+14*x+9*x^2)/(x-1)^4. - R. J. Mathar, Sep 19 2010
Sum_{n>=0} 1/a(n) = Pi^2/4 - log(4).
Sum_{n>=0} (-1)^n/a(n) = 2*G + log(2) - Pi/2, where G is the Catalan constant (A006752). (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {18, 75, 196, 405}, {0, 20}] (* Eric W. Weisstein, Dec 20 2017 *)
CoefficientList[Series[(1 + 14 x + 9 x^2)/(-1 + x)^4, {x, 0, 20}], x] (* Eric W. Weisstein, Dec 20 2017 *)
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PROG
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(PARI) a(n) = (n+1)*(2*n+1)^2; \\ Altug Alkan, Dec 20 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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