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A055845
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a(n)=4a(n-1)-a(n-2); a(0)=1, a(1)=8.
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2
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1, 8, 31, 116, 433, 1616, 6031, 22508, 84001, 313496, 1169983, 4366436, 16295761, 60816608, 226970671, 847066076, 3161293633, 11798108456, 44031140191, 164326452308, 613274669041, 2288772223856
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n)={8*[(2+sqrt(3))^n-(2-sqrt(3))^n]-[(2+sqrt(3))^(n-1) -(2-sqrt(3))^(n-1)]}/(2*sqrt(3)).
3*A144721(n)^2 - 11 = a(n)^2 - Sture Sjöstedt, Nov 30 2011
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EXAMPLE
| G.f.(x)=(1+4x)/(1-4x+x^2).
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MATHEMATICA
| LinearRecurrence[{4, -1}, {1, 8}, 50] (* Sture Sjöstedt, Nov 30 2011 *)
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CROSSREFS
| Cf. A054485.
Sequence in context: A115004 A005338 A006322 * A034556 A121097 A121093
Adjacent sequences: A055842 A055843 A055844 * A055846 A055847 A055848
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, May 31 2000
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