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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 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196. LINKS 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 (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). PROG (PARI) Vec((1+4*x)/(1-3*x+x^2) + O(x^40)) \\ Michel Marcus, Sep 06 2017 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 September 22 19:04 EDT 2018. Contains 315270 sequences. (Running on oeis4.)