A110225 Expansion of (-1+3*x+2*x^2-8*x^3+3*x^5-2*x^6-2*x^7+x^8) / ((x-1)*(x+1)*(x^2-2*x-1)*(x^2+2*x-1)).

1, -3, 5, -13, 28, -73, 164, -421, 956, -2449, 5572, -14269, 32476, -83161, 189284, -484693, 1103228, -2824993, 6430084, -16465261, 37477276, -95966569, 218433572, -559334149, 1273124156, -3260038321, 7420311364, -19000895773, 43248744028, -110745336313

Offset

0,2

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4baseksigcycsumseq[A*B] with A = + 'i + .5'ii' + .5'jj' + .5'kk' + .5e and B = - .25'j + .25'k - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e; sumtype: (Y[15], *, sum/2)

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,7,0,-7,0,1).

Formula

a(n) = -5*A000129(n+1) +12*A000129(n) -1/2 +(-1)^n/2 +(-1)^n*A000129(n+1), if n>2. - R. J. Mathar, Nov 10 2009

a(n) = 7*a(n-2) - 7*a(n-4) + a(n-6) for n>8. - Colin Barker, May 16 2019

Prog

(PARI) Vec((1 - 3*x - 2*x^2 + 8*x^3 - 3*x^5 + 2*x^6 + 2*x^7 - x^8) / ((1 - x)*(1 + x)*(1 + 2*x - x^2)*(1 - 2*x - x^2)) + O(x^30)) \\ Colin Barker, May 16 2019

Crossrefs

Sequence in context: A160823 A077443 A147196 * A065047 A282565 A295617

Adjacent sequences: A110222 A110223 A110224 * A110226 A110227 A110228

Keyword

easy,sign

Author

Creighton Dement, Sep 06 2005

Status

approved