A111642 Expansion of 2*(x-1)*(x+1)/((x^2+4*x+1)*(x^2-2*x-1)).

2, -12, 54, -224, 890, -3452, 13198, -50016, 188498, -707916, 2652678, -9925760, 37105802, -138631292, 517742494, -1933118784, 7216615970, -26937891852, 100545928278, -375272321696, 1400607336218, -5227311479036, 19509011469358, -72809634633120, 271731700422002

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: 1ibaseseq[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. A111639, A111640, A111641, A111643, A111644, A000126.

Programs

PARI

Vec(2*(1 - x)*(1 + x) / ((1 + 2*x - x^2)*(1 + 4*x + x^2)) + O(x^25)) \\ Colin Barker, Apr 29 2019

Formula

a(n) = -6*a(n-1) - 8*a(n-2) + 2*a(n-3) + a(n-4) for n>3. - Colin Barker, Apr 29 2019