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Search: id:A124124
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| A124124 |
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Nonnegative integers n such that 2n^2+2n-3 is square. |
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+0
2
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| 1, 2, 6, 13, 37, 78, 218, 457, 1273, 2666, 7422, 15541, 43261, 90582, 252146, 527953, 1469617, 3077138, 8565558
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For squares of the form 2n^2-2n-3, the answer is b(n) = 1 + a(n). - Zak Seidov Dec 04 2006.
First differences are apparently in A143608. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]
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FORMULA
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It appears that a(n)=2a(n-1)-2a(n-2)+a(n-3) if n is even, a(n)=5a(n-1)-5a(n-2)+a(n-3) if n is odd. Can anyone confirm this?
Yes, these formulae are correct. Also a(i) = 7*(a(i-2) - a(i-4)) + a(i-6) for i >= 7. - Zak Seidov Dec 04 2006
2*a(n)=sqrt[7+2*A077442(n-1)^2]-1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 03 2006
a(n)=a(n-1)+6*a(n-2)-6*a(n-3)-a(n-4)+a(n-5). G.f.: -x*(1+x-2*x^2+x^3+x^4)/((x-1)*(x^2-2*x-1)*(x^2+2*x-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]
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CROSSREFS
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Cf. A001108, A046172, A008844.
Adjacent sequences: A124121 A124122 A124123 this_sequence A124125 A124126 A124127
Sequence in context: A116426 A162057 A026550 this_sequence A052450 A001373 A057243
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Nov 29 2006
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