A154240 a(n) = ( (8 + sqrt(6))^n - (8 - sqrt(6))^n )/(2*sqrt(6)).

1, 16, 198, 2240, 24356, 259776, 2743768, 28833280, 302193936, 3162772736, 33077115488, 345793029120, 3614215767616, 37771456592896, 394718790964608, 4124756173045760, 43102408892784896, 450402684247904256

Offset

1,2

Comments

lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(6) = 10.4494897427....

Links

Harvey P. Dale, Table of n, a(n) for n = 1..981

Index entries for linear recurrences with constant coefficients, signature (16, -58).

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 16*a(n-1) - 58*a(n-2) for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 16*x + 58*x^2). (End)

E.g.f.: sinh(sqrt(6)*x)*exp(8*x)/sqrt(6). - Ilya Gutkovskiy, Sep 07 2016

Mathematica

Join[{a=1, b=16}, Table[c=16*b-58*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)
With[{s=Sqrt[6]}, Table[Simplify[((8+s)^n-(8-s)^n)/(2s)], {n, 20}]] (* or *) LinearRecurrence[{16, -58}, {1, 16}, 20] (* Harvey P. Dale, Jul 17 2013 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); 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. A010464 (decimal expansion of square root of 6).

Sequence in context: A153885 A016226 A332854 * A081679 A154249 A226869

Adjacent sequences: A154237 A154238 A154239 * A154241 A154242 A154243

Keyword

nonn

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