A153598 a(n) = ((7 + sqrt(3))^n - (7 - sqrt(3))^n)/(2*sqrt(3)).

1, 14, 150, 1456, 13484, 121800, 1084936, 9586304, 84301200, 739246816, 6471600224, 56597049600, 494665084096, 4321846895744, 37751262672000, 329712720203776, 2879419999940864, 25145094869798400, 219578008179897856, 1917417750507843584

Offset

1,2

Comments

lim_{n -> infinity} a(n)/a(n-1) = 7 + sqrt(3) = 8.73205080756887729....

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (14,-46).

Formula

G.f.: x/(1 - 14*x + 46*x^2). - Klaus Brockhaus, Dec 31 2008, (corrected Oct 11 2009)

a(n) = 14*a(n-1) - 46*a(n-2) for n>1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009

Mathematica

Join[{a=1, b=14}, Table[c=14*b-46*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{14, -46}, {1, 14}, 20] (* Harvey P. Dale, Dec 05 2015 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008
(Magma) I:=[1, 14]; [n le 2 select I[n] else 14*Self(n-1)-46*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 23 2016

Crossrefs

Cf. A002194 (decimal expansion of sqrt(3)).

Sequence in context: A019521 A009614 A009802 * A180347 A262183 A357484

Adjacent sequences: A153595 A153596 A153597 * A153599 A153600 A153601

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008

Extensions

Typo corrected and extended beyond a(7) by Klaus Brockhaus, Dec 31 2008

Edited by Klaus Brockhaus, Oct 11 2009

Status

approved