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 A153600 a(n) = ((9 + sqrt(3))^n - (9 - sqrt(3))^n)/(2*sqrt(3)). 1
 1, 18, 246, 3024, 35244, 398520, 4424328, 48553344, 528862608, 5732366112, 61931306592, 667638961920, 7186859400384, 77287630177152, 830602309958784, 8922406425440256, 95816335481139456, 1028746337476170240, 11043759907042186752, 118545464003618082816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(3) = 10.73205080756887729.... LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (18,-78). FORMULA G.f.: x/(1 - 18*x + 78*x^2). - Klaus Brockhaus, Dec 31 2008, (corrected Oct 11 2009) a(n) = 18*a(n-1) - 78*a(n-2) for n>1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009 MATHEMATICA Join[{a=1, b=18}, Table[c=18*b-78*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*) LinearRecurrence[{18, -78}, {1, 18}, 25] (* G. C. Greubel, Aug 22 2016 *) PROG (MAGMA) Z:= PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008 (MAGMA) I:=[1, 18]; [n le 2 select I[n] else 18*Self(n-1)-78*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 23 2016 CROSSREFS Cf. A002194 (decimal expansion of sqrt(3)). Sequence in context: A153593 A001713 A110395 * A016183 A016239 A153886 Adjacent sequences:  A153597 A153598 A153599 * A153601 A153602 A153603 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008 EXTENSIONS Extended beyond a(7) by Klaus Brockhaus, Dec 31 2008 Edited by Klaus Brockhaus, Oct 11 2009 STATUS approved

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Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)