A154236 a(n) = ( (5 + sqrt(6))^n - (5 - sqrt(6))^n )/(2*sqrt(6)).

1, 10, 81, 620, 4661, 34830, 259741, 1935640, 14421321, 107436050, 800355401, 5962269060, 44415937981, 330876267670, 2464859855061, 18361949464880, 136787157402641, 1018994534193690, 7590989351286721, 56548997363187100

Offset

1,2

Comments

First differences are in A164551.

Lim_{n -> infinity} a(n)/a(n-1) = 5 + sqrt(6) = 7.4494897427....

Links

G. C. Greubel, Table of n, a(n) for n = 1..999

Index entries for linear recurrences with constant coefficients, signature (10, -19).

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 10*a(n-1) - 19*a(n-2) for n > 1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 10*x + 19*x^2). (End)

Mathematica

LinearRecurrence[{10, -19}, {1, 10}, 25] (* or *) Table[Simplify[((5 + Sqrt[6])^n -(5-Sqrt[6])^n)/(2*Sqrt[6])], {n, 1, 25}] (* G. C. Greubel, Sep 06 2016 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((5+r)^n-(5-r)^n)/(2*r): n in [1..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
(Sage) [lucas_number1(n, 10, 19) for n in range(1, 25)] # Zerinvary Lajos, Apr 26 2009
(PARI) a(n)=([0, 1; -19, 10]^(n-1)*[1; 10])[1, 1] \\ Charles R Greathouse IV, Sep 07 2016

Crossrefs

Cf. A010464 (decimal expansion of square root of 6), A164551.

Sequence in context: A136870 A293367 A018202 * A095004 A037541 A037485

Adjacent sequences: A154233 A154234 A154235 * A154237 A154238 A154239

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 04 2009

Status

approved