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A055267 a(n) = 3a(n-1) - a(n-2); a(0)=1, a(1)=7. 2
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; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pp. 181-193.

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.

E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart.,7 (1969), pp. 231-242.

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) = (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).

G.f.: (1+4x)/(1-3x+x^2).

CROSSREFS

Cf. A054492, A054486.

Sequence in context: A047862 A264879 A048755 * A218843 A219422 A209546

Adjacent sequences:  A055264 A055265 A055266 * A055268 A055269 A055270

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 09 2000

STATUS

approved

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