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Search: id:A114695
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| A114695 |
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Three consecutive elements of the sequence built from a quadratic form over four consecutive Fibonacci numbers A000045. |
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6
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| 2, 2, 4, 104, 143, 169, 4895, 6764, 7921, 229970, 317810, 372100, 10803704, 14930351, 17480761, 507544127, 701408732, 821223649, 23843770274, 32951280098, 38580030724, 1120149658760, 1548008755919, 1812440220361
(list; graph; listen)
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OFFSET
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0,1
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FORMULA
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a(3*n) = (Fibonacci(4n) + Fibonacci(4n+1) )*Fibonacci(4n+3).
a(3n+1) = (Fibonacci(4n) + Fibonacci(4n+2) )*Fibonacci(4*n+3).
a(3n+2) = (Fibonacci(4n+1) + Fibonacci(4n+2) )*Fibonacci(4n+3).
a(3n)=A001654(4n+2). a(3n+1)= A128535(4n+3). a(3n+2)= A007598(4n+3). G.f.: -(2+2*x+4*x^2+8*x^3+47*x^4-23*x^5-x^6-4*x^7+x^8)/((x-1)*(1+x+x^2)*(x^6-47*x^3+1)). a(n)=48*a(n-3)-48*a(n-6)+a(n-9). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2009]
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MATHEMATICA
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F[0] = 0; F[1] = 1; F[n_] := F[n] = F[n - 1] + F[n - 2] a = Flatten[Table[{(F[4*n] + F[4*n + 1])*F[4*n + 3], (F[4*n] + F[4*n + 2])*F[4*n + 3], (F[4*n + 1] + F[4*n + 2])*F[4*n + 3]}, {n, 0, 12}]]
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CROSSREFS
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Cf. A000045.
Sequence in context: A050923 A067700 A037010 this_sequence A134084 A100247 A011342
Adjacent sequences: A114692 A114693 A114694 this_sequence A114696 A114697 A114698
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KEYWORD
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nonn,less
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 21 2006
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EXTENSIONS
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Edited by the Associate Editors of the OEIS, Sep 02 2009
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