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A132355
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Number of the form 9n^2+2n, n an integer.
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4
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0, 7, 11, 32, 40, 75, 87, 136, 152, 215, 235, 312, 336, 427, 455, 560, 592, 711, 747, 880, 920, 1067, 1111, 1272, 1320, 1495, 1547, 1736, 1792, 1995, 2055, 2272, 2336, 2567, 2635, 2880, 2952, 3211, 3287, 3560
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sequence allows us to find X values of the equation: 9*X^3 + X^2 = Y^2.
The set of all n such that 9n+1 is a perfect square [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 22 2010]
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REFERENCES
| Cooper, S. and Hirschhorn, M. D., Results of Hurwitz type for three squares. Discrete Math. 274 (2004), no. 1-3, 9-24. See BA(q).
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FORMULA
| a(2n) = n(9n+2), a(2n+1) = 9*n^2 + 16n + 7.
a(n) = n^2 + n + 5*ceiling(n/2)^2 [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 23 2010]
a(n)= +a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5). G.f.: x*(7+4*x+7*x^2)/ ((1+x)^2 * (1-x)^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2010]
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MAPLE
| readlib(issqr); for n from 0 to 3560 do if(issqr(9*n+1)) then print(n) fi od; [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 22 2010]
seq(n^2+n+5*ceil(n/2)^2, n=0..39); [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 23 2010]
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MATHEMATICA
| f[n_]:=IntegerQ[Sqrt[1+9*n]]; Select[Range[0, 8! ], f[ # ]&] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2010]
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CROSSREFS
| A205808 is the characteristic function.
Cf. A054000, A056220, A000217, A087475, A028347, A062717, A036666, A002378, A001082, A046092, A005563, A132209.
Cf. A010701, A056020 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A053711 A043110 A043890 * A019416 A138122 A176955
Adjacent sequences: A132352 A132353 A132354 * A132356 A132357 A132358
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KEYWORD
| nonn,changed
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AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 08 2007
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EXTENSIONS
| Simpler definition and minor edits from N. J. A. Sloane, Feb 03 2012
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