A154250 a(n) = ( (9 + sqrt(7))^n - (9 - sqrt(7))^n )/(2*sqrt(7)).

1, 18, 250, 3168, 38524, 459000, 5411224, 63436032, 741418000, 8651257632, 100857705376, 1175245632000, 13690951178176, 159468944439168, 1857310612720000, 21630889140461568, 251915019187028224

Offset

1,2

Comments

lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(7) = 11.6457513110....

Links

Harvey P. Dale, Table of n, a(n) for n = 1..938

Index entries for linear recurrences with constant coefficients, signature (18,-74).

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 18*a(n-1) - 74*a(n-2) for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 18*x + 74*x^2). (End)

Mathematica

Join[{a=1, b=18}, Table[c=18*b-74*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
LinearRecurrence[{18, -74}, {1, 18}, 20] (* Harvey P. Dale, Feb 16 2014 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); 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

Crossrefs

Cf. A010465 (decimal expansion of square root of 7).

Sequence in context: A016239 A153886 A154241 * A154350 A001722 A060788

Adjacent sequences: A154247 A154248 A154249 * A154251 A154252 A154253

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