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A084703
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Squares n such that 2n+1 is also a square.
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7
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0, 4, 144, 4900, 166464, 5654884, 192099600, 6525731524, 221682772224, 7530688524100, 255821727047184, 8690408031080164, 295218051329678400, 10028723337177985444, 340681375412721826704, 11573138040695364122500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| With the exception of 0, a subsequence of A075114. - R. J. Mathar, Dec 15 2008
Consequently A014105(k) is a square if and only if k = a(n). - Bruno Berselli, Oct 14 2011
Bissection of A079291. The squares 2n+1 are given in A055792. - M. F. Hasler, Jan 17 2012
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LINKS
| D. W. Wilson, Table of n, a(n-1) for n = 1..100 (offset=1)
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FORMULA
| a(n) = 4*A001110(n) = A001542(n)^2.
a(n+1) = A001652(n)*A001652(n+1) + A046090(n)*A046090(n+1) = A001542(n+1)^2. - Charlie Marion, 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, Jul 16 2003
G.f.: 4*x*(1+x)/((1-x)*(1-34*x+x^2)). - R. J. Mathar, Dec 15 2008
a(n)=A079291(2n). - M. F. Hasler, Jan 16 2012
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MATHEMATICA
| 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
| Cf. A084702, A001110.
A204576 is this sequence written in binary. - M. F. Hasler, Jan 17 2012
Sequence in context: A036511 A186720 A060870 * A186418 A122747 A069135
Adjacent sequences: A084700 A084701 A084702 * A084704 A084705 A084706
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 08 2003
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EXTENSIONS
| Edited and extended by Robert G. Wilson v, Jun 15 2003
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