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A055845 a(n) = 4a(n-1) - a(n-2); a(0)=1, a(1)=8. 3
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; 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..21.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (4,-1).

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

EXAMPLE

G.f.: (1+4x)/(1-4x+x^2).

MATHEMATICA

LinearRecurrence[{4, -1}, {1, 8}, 50]  (* Sture Sjöstedt, Nov 30 2011 *)

CROSSREFS

Cf. A054485.

Sequence in context: A212064 A213764 A289613 * A034556 A121097 A121093

Adjacent sequences:  A055842 A055843 A055844 * A055846 A055847 A055848

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 31 2000

STATUS

approved

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Last modified November 17 19:53 EST 2017. Contains 294834 sequences.