A154249 a(n) = ( (8 + sqrt(7))^n - (8 - sqrt(7))^n )/(2*sqrt(7)).

1, 16, 199, 2272, 25009, 270640, 2904727, 31049152, 331216993, 3529670224, 37595354983, 400334476960, 4262416397329, 45379597170544, 483115820080951, 5143216082574208, 54753855576573121, 582898372518440080

Offset

1,2

Comments

lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(7) = 10.6457513110....

Links

G. C. Greubel, Table of n, a(n) for n = 1..750

Index entries for linear recurrences with constant coefficients, signature (16, -57).

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 16*a(n-1)-57*a(n-2) for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 16*x + 57*x^2). (End)

E.g.f.: (1/sqrt(7))*exp(8*x)*sinh(sqrt(7)*x). - G. C. Greubel, Sep 08 2016

Maple

seq(expand((8+sqrt(7))^n-(8-sqrt(7))^n)/sqrt(28), n = 1 .. 20); # Emeric Deutsch, Jan 08 2009

Mathematica

Join[{a=1, b=16}, Table[c=16*b-57*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
LinearRecurrence[{16, -57}, {1, 16}, 25] (* or *) Table[( (8 + sqrt(7))^n - (8 - sqrt(7))^n )/(2*sqrt(7)), {n, 1, 25}] (* G. C. Greubel, Sep 08 2016 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); 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. A010465 (decimal expansion of square root of 7).

Sequence in context: A332854 A154240 A081679 * A226869 A257289 A125451

Adjacent sequences: A154246 A154247 A154248 * A154250 A154251 A154252

Keyword

nonn

Author

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

Extensions

Extended by Emeric Deutsch and Klaus Brockhaus, Jan 08 2009

Edited by Klaus Brockhaus, Oct 06 2009

Status

approved