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Search: id:A084703
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| A084703 |
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Squares n such that 2n+1 is also a square. |
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+0
6
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| 0, 4, 144, 4900, 166464, 5654884, 192099600, 6525731524, 221682772224, 7530688524100, 255821727047184, 8690408031080164, 295218051329678400, 10028723337177985444, 340681375412721826704, 11573138040695364122500
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = 4*A001110(n).
With the exception of 0, a subsequence of A075114. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 15 2008]
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FORMULA
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a(n+1) = A001652(n)*A001652(n+1) + A046090(n)*A046090(n+1) = A001542(n+1)^2 - Charlie Marion (charliem(AT)bestweb.net), Jul 01 2003
For k>=n>=0, a(n) = A001653(k+n)*A001653(k-n) - A001653(k)^2; e.g. 144 = 5741*5 - 169^2 - Charlie Marion (charliem(AT)bestweb.net), Jul 16 2003
G.f.: 4x(1+x)/((1-x)(1-34x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 15 2008]
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MATHEMATICA
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a[0] = 0; a[1] = 1; a[n_] := 34a[n - 1] - a[n - 2] + 2; Table[ 4a[n], {n, 0, 15}]
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CROSSREFS
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Cf. A084702, A001110.
a(n)=A001542(n)^2
Sequence in context: A134631 A036511 A060870 this_sequence A122747 A069135 A138176
Adjacent sequences: A084700 A084701 A084702 this_sequence A084704 A084705 A084706
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 08 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 15 2003
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