A111641 Expansion of -(1+x+3*x^2+x^3)/((x^2+4*x+1)*(x^2-2*x-1)).

1, -5, 25, -107, 433, -1697, 6529, -24839, 93841, -352973, 1323961, -4957139, 18539041, -69282185, 258790465, -966364367, 3607837153, -13467809237, 50270219929, -187629535739, 700287673681, -2613617125553, 9754412512321, -36404592257879, 135865306871281

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: 1lestesseq[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, A111642, A111643, A111644, A000126.

Programs

Mathematica

CoefficientList[Series[-(1+x+3x^2+x^3)/((x^2+4x+1)(x^2-2x-1)),{x,0,30}],x] (* or *) LinearRecurrence[{-6,-8,2,1},{1,-5,25,-107},30] (* Harvey P. Dale, Oct 12 2017 *)

PARI

Vec((1 + x + 3*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