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Search: id:A129556
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| A129556 |
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Numbers n such that centered pentagonal number A005891(n) = (5n^2+5n+2)/2 is a perfect square. |
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+0
5
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| 0, 2, 21, 95, 816, 3626, 31005, 137711, 1177392, 5229410, 44709909, 198579887, 1697799168, 7540806314, 64471658493, 286352060063, 2448225223584, 10873837476098, 92968086837717, 412919472031679, 3530339074609680
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Corresponding numbers k>0 such that k^2 is a centered pentagonal number are listed in A129557(n) = {1, 4, 34, 151, 1291, 5734, 49024, ...}.
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LINKS
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Eric Weisstein, Link to a section of The World of Mathematics, Centered Pentagonal Number.
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FORMULA
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For n>=5, a(n) = 38*a(n-2) - a(n-4) + 18 [From Max Alekseyev (maxale(AT)gmail.com), May 08 2009]
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MAPLE
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A005891 := proc(n) (5*n^2+5*n+2)/2 ; end: n := 0 : while true do if issqr(A005891(n)) then print(n) ; fi ; n := n+1 ; od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
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MATHEMATICA
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Do[ f=(5n^2+5n+2)/2; If[ IntegerQ[ Sqrt[f] ], Print[n] ], {n, 1, 40000} ]
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CROSSREFS
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Cf. A005891 = Centered pentagonal numbers: (5n^2+5n+2)/2. Cf. A129557 = numbers k>0 such that k^2 is a centered pentagonal number.
Sequence in context: A075681 A034520 A111128 this_sequence A077209 A068045 A079840
Adjacent sequences: A129553 A129554 A129555 this_sequence A129557 A129558 A129559
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 20 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
Formula and further terms from Max Alekseyev (maxale(AT)gmail.com), May 08 2009
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