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A055273 a(n) = 3a(n-1) - a(n-2); a(0)=1, a(1)=8. 2
1, 8, 23, 61, 160, 419, 1097, 2872, 7519, 19685, 51536, 134923, 353233, 924776, 2421095, 6338509, 16594432, 43444787, 113739929, 297775000, 779585071, 2040980213, 5343355568, 13989086491, 36623903905, 95882625224 (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, pp. 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) = (8*(((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.: (1+5x)/(1-3x+x^2).

CROSSREFS

Cf. A055267.

Sequence in context: A048467 A002765 A048770 * A241353 A059209 A099274

Adjacent sequences:  A055270 A055271 A055272 * A055274 A055275 A055276

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 28 2000

STATUS

approved

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Last modified January 24 12:17 EST 2017. Contains 281237 sequences.