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A132356
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Sequence allows us to find X values of the equation: 10*X^3 + X^2 = Y^2.
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1
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0, 8, 12, 36, 44, 84, 96, 152, 168, 240, 260, 348, 372, 476, 504, 624, 656, 792, 828, 980, 1020, 1188, 1232, 1416, 1464, 1664, 1716, 1932, 1988, 2220, 2280, 2528, 2592, 2856, 2924, 3204, 3276, 3572, 3648, 3960, 4040, 4368, 4452, 4796, 4884, 5244, 5336, 5712
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Polygonal number connection: 2H_n + 6S_n where H_n is the n-th hexagonal number and S_n is the n-th square number. This is the base formula that is expanded upon to achieve the full series. See contributing formula below. [From William A. Tedeschi (fynmun(AT)att.net), Sep 12 2010]
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FORMULA
| a(2n)=n(10n+2), a(2n+1)=10*n^2 + 18n + 8.
O.g.f.: 4x(2x^2+x+2)/[(1-x)^3*(1+x)^2]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2008
a(n) = 10x^2 - 2x where x = floor(n/2)*(-1)^n for n >= 1. [From William A. Tedeschi (fynmun(AT)att.net), Sep 12 2010]
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MATHEMATICA
| s=0; lst={}; Do[s+=(4*n/5); If[IntegerQ[s], AppendTo[lst, s]], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 26 2009]
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CROSSREFS
| Cf. A054000, A056220, A000217, A087475, A028347, A062717, A036666, A002378, A001082, A046092, A005563, A132209.
Sequence in context: A137148 A045018 A067681 * A024604 A025103 A092179
Adjacent sequences: A132353 A132354 A132355 * A132357 A132358 A132359
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KEYWORD
| nonn
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AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 08 2007
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Nov 13 2009
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