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 A055269 a(n) = 4*a(n-1) - a(n-2) + 3; a(0)=1, a(1)=7. 0
 1, 7, 30, 116, 437, 1635, 6106, 22792, 85065, 317471, 1184822, 4421820, 16502461, 61588027, 229849650, 857810576, 3201392657, 11947760055, 44589647566, 166410830212, 621053673285, 2317803862931, 8650161778442, 32282843250840, 120481211224921, 449642001648847 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also partial sums of A054491. 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. Index entries for linear recurrences with constant coefficients, signature (5,-5,1). FORMULA G.f.: (1+2x)/((1-x)(1-4x+x^2)). a(n) = (((17-5*(2-sqrt(3)))(2+sqrt(3))^n+(5*(2+sqrt(3))-17)(2-sqrt(3))^n)/(4*sqrt(3))) - 3/2. MATHEMATICA LinearRecurrence[{5, -5, 1}, {1, 7, 30}, 40] (* or *) CoefficientList[ Series[ (-1-2*x)/(-1+5*x-5*x^2+x^3), {x, 0, 40}], x] (* Harvey P. Dale, Dec 01 2013 *) CROSSREFS Cf. A001834, A054491. Sequence in context: A062455 A085277 A269084 * A026631 A037709 A037611 Adjacent sequences:  A055266 A055267 A055268 * A055270 A055271 A055272 KEYWORD easy,nonn AUTHOR Barry E. Williams, May 10 2000 EXTENSIONS Corrected by T. D. Noe, Nov 07 2006 STATUS approved

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Last modified July 23 13:49 EDT 2019. Contains 325254 sequences. (Running on oeis4.)