A107334 G.f.: (3-4*x-3*x^2)/(1-2*x-3*x^2+2*x^3).

3, 2, 10, 20, 66, 172, 502, 1388, 3938, 11036, 31110, 87452, 246162, 692460, 1948502, 5482060, 15424706, 43398588, 122107174, 343560700, 966645746, 2719759244, 7652334326, 21530654892, 60578794274, 170444884572, 479564842182, 1349306749532, 3796418256466

Offset

0,1

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (2,3,-2).

Formula

a(n)=b1^n+b2^n+b3^n where b1, b2, b3 are the roots of x^3-2*x^2-3*x+2.

Limit a[n]/a[n-1] as n -> infinity is the largest root.

Mathematica

b3 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[3]] b2 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[2]] b1 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[1]] digits = 25 a = Table[2*(b3^n + b1^n + b2^n)/(b3 + b2 + b1), {n, 0, digits}]

Prog

(PARI) a(n)=if(n<0, 0, polsym(x^3-2*x^2-3*x+2, n)[n+1])
(PARI) a(n)=([0, 1, 0; 0, 0, 1; -2, 3, 2]^n*[3; 2; 10])[1, 1] \\ Charles R Greathouse IV, Jul 21 2016

Crossrefs

Sequence in context: A082219 A034461 A070033 * A335719 A096073 A088302

Adjacent sequences: A107331 A107332 A107333 * A107335 A107336 A107337

Keyword

nonn,easy

Author

Roger L. Bagula, May 22 2005

Extensions

Edited by N. J. A. Sloane, Jun 08 2007

Status

approved