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 A154249 a(n) = ( (8 + sqrt(7))^n - (8 - sqrt(7))^n )/(2*sqrt(7)). 1
 1, 16, 199, 2272, 25009, 270640, 2904727, 31049152, 331216993, 3529670224, 37595354983, 400334476960, 4262416397329, 45379597170544, 483115820080951, 5143216082574208, 54753855576573121, 582898372518440080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(7) = 10.6457513110.... LINKS G. C. Greubel, Table of n, a(n) for n = 1..750 Index entries for linear recurrences with constant coefficients, signature (16, -57). FORMULA From Philippe Deléham, Jan 06 2009: (Start) a(n) = 16*a(n-1)-57*a(n-2) for n>1, with a(0)=0, a(1)=1. G.f.: x/(1 - 16*x + 57*x^2). (End) E.g.f.: (1/sqrt(7))*exp(8*x)*sinh(sqrt(7)*x). - G. C. Greubel, Sep 08 2016 MAPLE seq(expand((8+sqrt(7))^n-(8-sqrt(7))^n)/sqrt(28), n = 1 .. 20); # Emeric Deutsch, Jan 08 2009 MATHEMATICA Join[{a=1, b=16}, Table[c=16*b-57*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *) LinearRecurrence[{16, -57}, {1, 16}, 25] (* or *) Table[( (8 + sqrt(7))^n - (8 - sqrt(7))^n )/(2*sqrt(7)), {n, 1, 25}] (* G. C. Greubel, Sep 08 2016 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-7); S:=[ ((8+r)^n-(8-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009 CROSSREFS Cf. A010465 (decimal expansion of square root of 7). Sequence in context: A016226 A154240 A081679 * A226869 A257289 A125451 Adjacent sequences:  A154246 A154247 A154248 * A154250 A154251 A154252 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009 EXTENSIONS Extended by Emeric Deutsch and Klaus Brockhaus, Jan 08 2009 Edited by Klaus Brockhaus, Oct 06 2009 STATUS approved

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Last modified July 15 20:00 EDT 2019. Contains 325056 sequences. (Running on oeis4.)