A154241 a(n) = ( (9 + sqrt(6))^n - (9 - sqrt(6))^n )/(2*sqrt(6)).

1, 18, 249, 3132, 37701, 443718, 5159349, 59589432, 685658601, 7872647418, 90283258449, 1034650095732, 11852457339501, 135745474931118, 1554484248297549, 17799805849522032, 203810186669080401

Offset

1,2

Comments

lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(6) = 11.4494897427....

Links

G. C. Greubel, Table of n, a(n) for n = 1..925

Index entries for linear recurrences with constant coefficients, signature (18,-75).

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 18*a(n-1) - 75*a(n-2) for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 18*x + 75*x^2). (End)

E.g.f.: sinh(sqrt(6)*x)*exp(9*x)/sqrt(6). - Ilya Gutkovskiy, Sep 07 2016

Mathematica

Join[{a=1, b=18}, Table[c=18*b-75*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
LinearRecurrence[{18, -75}, {1, 18}, 25] (* or *) Table[( (9 + sqrt(6))^n - (9 - sqrt(6))^n )/(2*sqrt(6)), {n, 1, 25}] (* G. C. Greubel, Sep 07 2016 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
(PARI) a(n)=([0, 1; -75, 18]^(n-1)*[1; 18])[1, 1] \\ Charles R Greathouse IV, Jun 04 2026

Crossrefs

Cf. A010464 (decimal expansion of square root of 6).

Sequence in context: A016183 A016239 A153886 * A385029 A154250 A154350

Adjacent sequences: A154238 A154239 A154240 * A154242 A154243 A154244

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009

Extensions

Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009

Edited by Klaus Brockhaus, Oct 06 2009

Status

approved