A110158 Expansion of x^4 / ((x+1)*(2*x^3-2*x^2-2*x+1)*(x-1)^2).

0, 0, 0, 0, 1, 3, 10, 26, 69, 173, 436, 1084, 2699, 6699, 16634, 41274, 102425, 254137, 630584, 1564600, 3882103, 9632247, 23899510, 59299318, 147133173, 365065973, 905799668, 2247464948, 5576397299, 13836125171

Offset: 0

Author

Creighton Dement, Sep 05 2005

Keywords

• nonn
• easy

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1jbasejcycsumseq[ + .5'k + .5k' + 'ij'], sumtype: (Y[15], *, vesy)

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,1,-7,2,4,-2).

Crossrefs

Cf. A077847.

Programs

Mathematica

CoefficientList[Series[x^4/((x+1)(2x^3-2x^2-2x+1)(x-1)^2),{x,0,30}],x] (* Harvey P. Dale, Jan 23 2019 *)

PARI

concat([0,0,0,0], Vec(x^4 / ((1 - x)^2*(1 + x)*(1 - 2*x - 2*x^2 + 2*x^3)) + O(x^40))) \\ Colin Barker, May 16 2019

Formula

a(n) = -(-1)^n/4 + 7/4 - A077937(n) + A077937(n-1) + 4*A077937(n-2) - (n+1)/2. - R. J. Mathar, Nov 10 2009

a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + 2*a(n-4) + 4*a(n-5) - 2*a(n-6) for n > 5. - Colin Barker, May 16 2019