A153600 a(n) = ((9 + sqrt(3))^n - (9 - sqrt(3))^n)/(2*sqrt(3)).

1, 18, 246, 3024, 35244, 398520, 4424328, 48553344, 528862608, 5732366112, 61931306592, 667638961920, 7186859400384, 77287630177152, 830602309958784, 8922406425440256, 95816335481139456, 1028746337476170240, 11043759907042186752, 118545464003618082816

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<x>:= PolynomialRing(Integers()); N<r>:=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