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Search: id:A054489
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| A054489 |
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A second order recursive sequence. |
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+0
3
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| 1, 10, 59, 344, 2005, 11686, 68111, 396980, 2313769, 13485634, 78600035, 458114576, 2670087421, 15562409950, 90704372279, 528663823724, 3081278570065, 17959007596666, 104672767009931, 610077594462920
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7(1969), pps. 181-193.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N. Y., 1964, pps. 122-125, 194-196.
E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7(1969), pps. 231-242.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=6a(n-1)-a(n-2), a(0)=1, a(1)=10.
a(n)={10*([3+2sqrt(2)]^n-[3-2sqrt(2)]^n)-([3+2sqrt(2)]^(n-1)-[3-2sqrt(2)]^(n-1))}/4sqrt(2).
G.f.: (1+4*x)/(1-6*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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MAPLE
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a[0]:=1: a[1]:=10: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006
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CROSSREFS
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Cf. A054488 and A038761.
Sequence in context: A045950 A061001 A055586 this_sequence A140890 A055714 A046762
Adjacent sequences: A054486 A054487 A054488 this_sequence A054490 A054491 A054492
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, May 04 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 05 2000
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