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A101180
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Numbers n such that 19*n^2 + 19*n + 1 is a square.
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3
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0, 8, 671, 15639, 42159, 981911, 77624048, 1807894920, 4873553880, 113507005568, 8973184757831, 208989037004319, 563373081435879, 13121182828725551, 1037282211558181688, 24158714697817430640, 65124801462951244560, 1516782492521509296728
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OFFSET
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1,2
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COMMENTS
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Define a(1)=0, a(2)=8, a(3)=671, a(4)=15639, a(5)=42159, a(6)=981911, the first 6 terms found for the sequence then a(7)=57799*(2*a(3)+1)-a(2)-1, a(8)=57799*(2*a(4)+1)-a(1)-1 for n>8 a(n)=57799*(2*a(n-4)+1)-a(n-8)-1 remark:57799 = 38*39*39+1 =2*19*(39^2)+1
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LINKS
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Table of n, a(n) for n=1..18.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,115598,-115598,0,0,-1,1).
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FORMULA
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G.f.: -x^2*(8*x^6+663*x^5+14968*x^4+26520*x^3+14968*x^2+663*x+8) / ((x-1)*(x^4-340*x^2+1)*(x^4+340*x^2+1)). - Colin Barker, Mar 05 2013
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CROSSREFS
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Cf. A105839.
Sequence in context: A099126 A172919 A286394 * A128875 A199801 A278857
Adjacent sequences: A101177 A101178 A101179 * A101181 A101182 A101183
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KEYWORD
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nonn,easy
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AUTHOR
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Pierre CAMI, Apr 06 2005, Apr 22 2005
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EXTENSIONS
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Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar
More terms (using recursive formula in comment) from Jon E. Schoenfield, Jul 10 2010
a(18) from Colin Barker, Mar 05 2013
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STATUS
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approved
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