A111640 Expansion of (-1+3*x+x^2-x^3)/((x^2+4*x+1)*(x^2-2*x-1)).

1, -9, 45, -195, 793, -3117, 12013, -45751, 172961, -650849, 2441917, -9144539, 34203161, -127829669, 477505565, -1783134255, 6657304833, -24851573497, 92762239373, -346229372851, 1292232479961, -4822886991709, 17999765604237, -67177262104679, 250711906290721

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: 1vesseq[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, A111641, A111642, A111643, A000126.

Programs

PARI

Vec((1 - 3*x - x^2 + x^3) / ((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