A111643 Expansion of 2*(x+1)^2/((x^2+4*x+1)*(x^2-2*x-1)).

-2, 8, -34, 136, -530, 2032, -7714, 29104, -109378, 410040, -1534722, 5738360, -21441682, 80083808, -299027394, 1116348896, -4167148290, 15554127592, -58053908834, 216672484584, -808662529938, 3018041612880, -11263658377442, 42036964786320, -156885101002562

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: 1baseiseq[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, A111642, A111644, A000126.

Programs

PARI

Vec(-2*(1 + x)^2 / ((1 + 2*x - x^2)*(1 + 4*x + x^2)) + O(x^40)) \\ Colin Barker, May 01 2019

Formula

From Colin Barker, May 01 2019: (Start)

a(n) = (-3*(-1-sqrt(2))^(1+n) - 3*(-1+sqrt(2))^(1+n) - 9*(-2-sqrt(3))^n - 5*sqrt(3)*(-2-sqrt(3))^n - 9*(-2+sqrt(3))^n + 5*sqrt(3)*(-2+sqrt(3))^n) / 6.

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

(End)