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A055271 a(n) = 5a(n-1) - a(n-2); a(0)=1, a(1)=7. 3
1, 7, 34, 163, 781, 3742, 17929, 85903, 411586, 1972027, 9448549, 45270718, 216905041, 1039254487, 4979367394, 23857582483, 114308545021, 547685142622, 2624117168089, 12572900697823, 60240386321026, 288629030907307 (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. 122-125, 194-196.

LINKS

Table of n, a(n) for n=0..21.

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

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

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (5,-1).

FORMULA

a(n) = (7*(((5+sqrt(21))/2)^n - ((5-sqrt(21))/2)^n) - (((5+sqrt(21))/2)^(n-1) - ((5-sqrt(21))/2)^(n-1)))/sqrt(21).

G.f.: (1+2*x)/(1-5*x+x^2).

a(n) = (-1)^n*Sum_{k = 0..n} A238731(n,k)*(-8)^k. - Philippe Deléham, Mar 05 2014

CROSSREFS

Cf. A030221.

Sequence in context: A099242 A032206 A124466 * A209890 A027209 A209807

Adjacent sequences:  A055268 A055269 A055270 * A055272 A055273 A055274

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 10 2000

STATUS

approved

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Last modified August 19 23:35 EDT 2017. Contains 290821 sequences.