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Search: id:A141530
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| 1, -1, 9, 55, 161, 351, 649, 1079, 1665, 2431, 3401, 4599, 6049, 7775, 9801, 12151, 14849, 17919, 21385, 25271, 29601, 34399, 39689, 45495, 51841, 58751, 66249, 74359, 83105, 92511, 102601, 113399, 124929, 137215, 150281, 164151, 178849, 194399, 210825, 228151
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Except for the two terms of [A141530] and the first term of [A046092[, if X=[A141530], A=[A078371], Y=[A046092], we have, for all others terms, Pell's equation: X^2-A*Y^2=1. Example: 9^2-5*4^2=1; 55^2-21*12^2=1; 161^2-45*24^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 13 2009]
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FORMULA
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a(n)=(2n-1)(2n^2-2n-1)=A060747(n)*A132209(n-1), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2009]
G.f.: (1-5*x+19*x^2+9*x^3)/(1-x)^4 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Aug 30 2009]
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MATHEMATICA
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Table[EulerE[3, n], {n, 0, 50}]*4; ..and/or..Array[4*#^3-6*#^2+1&, 50, 0] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 03 2009]
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CROSSREFS
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Cf. A141047, A141417.
Cf. A046092, A078371 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 13 2009]
Sequence in context: A058852 A145875 A068970 this_sequence A016269 A005770 A030053
Adjacent sequences: A141527 A141528 A141529 this_sequence A141531 A141532 A141533
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KEYWORD
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sign,less,new
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Aug 12 2008
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EXTENSIONS
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Corrected, completed and edited, following an observation from Vincenzo Librandi, by M. F. Hasler (MHasler(AT)univ-ag.frC), Feb 12 2009. Further edited by N. J. A. Sloane (njas(AT)research.att.com), Feb 13 2009
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