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A002537
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a(2n) = a(2n-1) + 3a(2n-2), a(2n+1) = 2a(2n) + 3a(2n-1).
(Formerly M3409 N1379)
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2
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1, 1, 4, 11, 23, 79, 148, 533, 977, 3553, 6484, 23627, 43079, 157039, 286276, 1043669, 1902497, 6936001, 12643492, 46094987, 84025463, 306335887, 558412276, 2035832213, 3711069041, 13529634721, 24662841844, 89914587851
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.
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LINKS
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FORMULA
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a(n)=8a(n-2)-9a(n-4). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
G.f.: (1+x-4x^2+3x^3)/(1-8x^2+9x^4). a(n)/A002536(n) converges to sqrt(7). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
a(n+1) = x^n + (-1)^n*(x-2)^n where x = (1+sqrt(7)) and the term is divided by 2 for a(2) and a(3), 4 for a(4) and a(5)... 2^n for a(2n) and a(2n+1). - Ben Paul Thurston, Aug 30 2006
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MAPLE
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A002537:=(1+z-4*z**2+3*z**3)/(1-8*z**2+9*z**4); # conjectured by Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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LinearRecurrence[{0, 8, 0, -9}, {1, 1, 4, 11}, 40] (* Harvey P. Dale, Jul 24 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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