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A055849 a(n) = 3a(n-1) - a(n-2); a(0)=1, a(1)=9. 3
1, 9, 26, 69, 181, 474, 1241, 3249, 8506, 22269, 58301, 152634, 399601, 1046169, 2738906, 7170549, 18772741, 49147674, 128670281, 336863169, 881919226, 2308894509, 6044764301, 15825398394, 41431430881, 108468894249 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.

LINKS

Table of n, a(n) for n=0..25.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (3,-1).

FORMULA

a(n) = (9*(((3+sqrt(5))/2)^n - ((3-sqrt(5))/2)^n) - (((3+sqrt(5))/2)^(n-1) - ((3-sqrt(5))/2)^(n-1)))/sqrt(5).

G.f.(x)=(1+6x)/(1-3x+x^2).

MATHEMATICA

LinearRecurrence[{3, -1}, {1, 9}, 40] (* Harvey P. Dale, Jan 20 2013 *)

CROSSREFS

Sequence in context: A048468 A255108 A048771 * A235163 A084813 A056409

Adjacent sequences:  A055846 A055847 A055848 * A055850 A055851 A055852

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jun 03 2000

STATUS

approved

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Last modified May 23 02:46 EDT 2017. Contains 286909 sequences.