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Search: id:A054492
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| A054492 |
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a(n)=3a(n-1)-a(n-2), a(0)=1,a(0)=6. |
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+0
3
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| 1, 6, 17, 45, 118, 309, 809, 2118, 5545, 14517, 38006, 99501, 260497, 681990, 1785473, 4674429, 12237814, 32039013, 83879225, 219598662, 574916761, 1505151621, 3940538102, 10316462685, 27008849953, 70710087174
(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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2*Lucas(2n+1) - Fibonacci(2n+1).
G.f.: (1+3*x)/(1-3*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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EXAMPLE
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a(n)={6*([(3+sqrt(5))/2]^n-[(3-sqrt(5))/2]^n)-([(3+sqrt(5))/2]^(n-1)-[(3-sqrt(5))/2]^(n-1))}/sqrt(5).
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CROSSREFS
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Cf. A002878 and A054486.
Sequence in context: A066183 A048746 A026382 this_sequence A128525 A083334 A088016
Adjacent sequences: A054489 A054490 A054491 this_sequence A054493 A054494 A054495
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, May 06 2000
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