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Search: id:A055267
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| A055267 |
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a(n)=3a(n-1)-a(n-2); a(0)=1, a(1)=7. |
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+0
3
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| 1, 7, 20, 53, 139, 364, 953, 2495, 6532, 17101, 44771, 117212, 306865, 803383, 2103284, 5506469, 14416123, 37741900, 98809577, 258686831, 677250916, 1773065917, 4641946835, 12152774588, 31816376929, 83296356199
(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)={7*[((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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EXAMPLE
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G.f.=(1+4x)/(1-3x+x^2)
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CROSSREFS
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Cf. A054492 and A054486.
Sequence in context: A007044 A047862 A048755 this_sequence A009370 A009372 A051102
Adjacent sequences: A055264 A055265 A055266 this_sequence A055268 A055269 A055270
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, May 09 2000
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