A111639 Expansion of (3+8*x-3*x^2-2*x^3)/((x^2+4*x+1)*(x^2-2*x-1)).

-3, 10, -33, 114, -403, 1450, -5281, 19394, -71619, 265450, -986241, 3670002, -13670803, 50957770, -190026433, 708824834, -2644492803, 9867263050, -36820012641, 137401810674, -512760729619, 1913577130090, -7141393334881, 26651623320002, -99464199710403

Offset: 0

Author

Creighton Dement, Aug 10 2005

Keywords

• easy
• sign

Comments

In reference to the program code, the sequence of Pell numbers A000126 is given by 1kbaseseq[C*J]. A001353 is 1ibaseiseq[C*J].

Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[C*J] with C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' and J = + j' + k' + 1.5'ii' + .5'jj' + .5'kk' + .5e

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-6,-8,2,1).

Crossrefs

Cf. A111640, A111641, A111642, A111643, A000126.

Programs

Mathematica

LinearRecurrence[{-6,-8,2,1},{-3,10,-33,114},30] (* Harvey P. Dale, Jul 04 2019 *)

PARI

Vec(-(3 + 8*x - 3*x^2 - 2*x^3) / ((1 + 2*x - x^2)*(1 + 4*x + x^2)) + O(x^25)) \\ Colin Barker, May 11 2019

Formula

From Colin Barker, May 11 2019: (Start)

a(n) = ((-1-sqrt(2))^(1+n) + (-1+sqrt(2))^(1+n) - 2*(-2-sqrt(3))^n - sqrt(3)*(-2-sqrt(3))^n - 2*(-2+sqrt(3))^n + sqrt(3)*(-2+sqrt(3))^n) / 2.

a(n) = -6*a(n-1) - 8*a(n-2) + 2*a(n-3) + a(n-4) for n>3. (End)