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Search: id:A126354
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| A126354 |
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a(1)=1, a(2)=0, a(3)=3, a(4)=2; for n > 4, a(n) = 6*a(n-2) - a(n-4). |
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+0
2
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| 1, 0, 3, 2, 17, 12, 99, 70, 577, 408, 3363, 2378, 19601, 13860, 114243, 80782, 665857, 470832, 3880899, 2744210, 22619537, 15994428, 131836323, 93222358, 768398401, 543339720, 4478554083, 3166815962, 26102926097, 18457556052, 152139002499
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Each pair {odd=x,even=y} terms gives solution to the Pell's equation x^2-2y^2=1. Note that odd/even terms have also odd/even indices. Ratio a(2k-1)/a(2k) tends to sqrt(2). Interrelations between odd and even terms: a(2k+1)=3a(2k-1)+4a(2k), e.g. 99=3*17+4*12, 577=3*99+4*70; a(2k)=3a(2k-2)+2a(2k-3), e.g., 70=3*12+2*17, 408=3*70+2*99. Odd terms = A001541, even terms = 2*A001109.
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FORMULA
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O.g.f.: x*(2*x+1)*(-1+x)^2/((x^2-2*x-1)*(x^2+2*x-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 10 2007
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CROSSREFS
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Cf. A001109, A001541.
Sequence in context: A084886 A055864 A072045 this_sequence A158939 A026345 A092644
Adjacent sequences: A126351 A126352 A126353 this_sequence A126355 A126356 A126357
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)gmail.com), Dec 26 2006
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