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A129445
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Numbers k>0 such that k^2 is a centered triangular number.
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5
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1, 2, 8, 19, 79, 188, 782, 1861, 7741, 18422, 76628, 182359, 758539, 1805168, 7508762, 17869321, 74329081, 176888042, 735782048, 1751011099, 7283491399, 17333222948, 72099131942, 171581218381, 713707828021, 1698478960862
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OFFSET
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1,2
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COMMENTS
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Corresponding numbers n such that centered triangular number A005448(n) is a perfect square are listed in A129444(n).
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LINKS
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_Alexander Adamchuk_, Apr 26 2007, Table of n, a(n) for n = 1..100
Tom Beldon and Tony Gardiner, Triangular Numbers and Perfect Squares, The Mathematical Gazette, Vol. 86, No. 507, (2002), pp. 423-431. [Ant King, Dec 07 2010]
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FORMULA
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a(n) = Sqrt[ 3*A129444(n)*(A129444(n) - 1)/2 + 1 ].
Empirical G.f.: x*(1-x)*(1+3*x+x^2)/(1-10*x^2+x^4). [Colin Barker, Apr 11 2012]
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MATHEMATICA
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Do[ f = 3n(n-1)/2 + 1; If[ IntegerQ[ Sqrt[f] ], Print[ Sqrt[f] ] ], {n, 1, 150000} ]
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CROSSREFS
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Cf. A005448, A129444.
Prime terms are listed in A129446.
Sequence in context: A026588 A026572 A074797 * A082821 A188893 A030097
Adjacent sequences: A129442 A129443 A129444 * A129446 A129447 A129448
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk, Apr 15 2007, Apr 26 2007
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EXTENSIONS
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More terms from Alexander Adamchuk, Apr 26 2007
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STATUS
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approved
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