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35, 143, 323, 575, 899, 1295, 1763, 2303, 2915, 3599, 4355, 5183, 6083, 7055, 8099, 9215, 10403, 11663, 12995, 14399, 15875, 17423, 19043, 20735, 22499, 24335, 26243, 28223, 30275, 32399, 34595, 36863, 39203, 41615, 44099, 46655, 49283, 51983
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A061037=0,5,3,21,2,45,15,77,6,117,35,: a(n)= A061037(12n+10)=(6n-1)*(6n+1)=36*n^2-1. From Balmer spectrum of hydrogen. [From Paul Curtz (bpcrtz(AT)free.fr), Sep 25 2008]
Sum_{k>=1} (-1)^(k+1)/a(k) = (Pi-3)/6 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 20 2009]
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LINKS
| Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
X. Gourdon and P. Sebah, Collection of series for Pi
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| O.g.f.: x*(-35-38*x+x^2)/(-1+x)^3 = 1-35/(-1+x)-108/(-1+x)^2-72/(-1+x)^3 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2007
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MATHEMATICA
| Table[36n^2 - 1, {n, 1, 100}]
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PROG
| (PARI) a(n)=36*n^2-1 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 20 2009]
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CROSSREFS
| Cf. A088878, A023208, A136016.
Sequence in context: A171473 A158586 A157286 * A048628 A048629 A133534
Adjacent sequences: A136014 A136015 A136016 * A136018 A136019 A136020
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KEYWORD
| nonn,easy
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 10 2007
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