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A054489 Expansion of (1+4x)/(1-6x+x^2). 4
1, 10, 59, 344, 2005, 11686, 68111, 396980, 2313769, 13485634, 78600035, 458114576, 2670087421, 15562409950, 90704372279, 528663823724, 3081278570065, 17959007596666, 104672767009931, 610077594462920 (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..19.

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 (6,-1).

FORMULA

a(n) = 6a(n-1) - a(n-2), a(0)=1, a(1)=10.

a(n) = (10*((3+2*sqrt(2))^n - (3-2*sqrt(2))^n) - ((3+2*sqrt(2))^(n-1) - (3-2*sqrt(2))^(n-1)))/(4*sqrt(2)).

MAPLE

a[0]:=1: a[1]:=10: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], n=0..19); # Zerinvary Lajos, Jul 26 2006

CROSSREFS

Cf. A054488, A038761.

Sequence in context: A226796 A061001 A055586 * A219580 A267021 A213346

Adjacent sequences:  A054486 A054487 A054488 * A054490 A054491 A054492

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 04 2000

EXTENSIONS

More terms from James A. Sellers, May 05 2000

STATUS

approved

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Last modified September 26 03:18 EDT 2017. Contains 292502 sequences.