A109782 Expansion of x*(1+2*x^2-2*x^3+x^4) / ((x-1)*(x^2-2*x-1)*(x^2-x+1)*(x+1)^2).

0, 1, -2, 8, -21, 54, -134, 329, -798, 1934, -4675, 11294, -27274, 65855, -158996, 383862, -926735, 2237348, -5401448, 13040263, -31481992, 76004268, -183490549, 442985388, -1069461348, 2581908109, -6233277590, 15048463316, -36330204249, 87708871842, -211747947962

Offset

0,3

Comments

Floretion Algebra Multiplication Program, FAMP Code: 2jbasesumseq[A*C] with A = + .5'k + .5k' + .5'ii' + .5'jj' and C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki'; sumtype: sum[Y[15]] = sum[ * ]

Links

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

Index entries for linear recurrences with constant coefficients, signature (-2,2,1,-3,2,2,-1).

Formula

From Colin Barker, May 15 2019: (Start)

G.f.: x*(1 + 2*x^2 - 2*x^3 + x^4) / ((1 - x)*(1 + x)^2*(1 + 2*x - x^2)*(1 - x + x^2)).

a(n) = -2*a(n-1) + 2*a(n-2) + a(n-3) - 3*a(n-4) + 2*a(n-5) + 2*a(n-6) - a(n-7) for n>6. (End)

Mathematica

LinearRecurrence[{-2, 2, 1, -3, 2, 2, -1}, {0, 1, -2, 8, -21, 54, -134}, 40] (* Harvey P. Dale, Mar 01 2023 *)

Prog

(PARI) concat(0, Vec(x*(1 + 2*x^2 - 2*x^3 + x^4) / ((1 - x)*(1 + x)^2*(1 + 2*x - x^2)*(1 - x + x^2)) + O(x^35))) \\ Colin Barker, May 15 2019

Crossrefs

Sequence in context: A034519 A014409 A303721 * A237268 A216893 A264245

Adjacent sequences: A109779 A109780 A109781 * A109783 A109784 A109785

Keyword

easy,sign

Author

Creighton Dement, Aug 13 2005

Status

approved