A107852 Expansion of -x*(x^2+1)*(x+1)^2/((2*x^3+x^2-1)*(x^4+1)).

0, 1, 2, 3, 6, 7, 10, 17, 22, 37, 58, 83, 134, 199, 298, 465, 694, 1061, 1626, 2451, 3750, 5703, 8650, 13201, 20054, 30501, 46458, 70611, 107462, 163527, 248682, 378449, 575734, 875813, 1332634, 2027283, 3084262, 4692551, 7138826, 10861073

Offset: 0

Author

Creighton Dement, May 25 2005

Keywords

• easy
• nonn

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1baseiforzapseq[(.5i' + .5j' + .5'ki' + .5'kj')*(.5'i + .5'j + .5'ik' + .5'jk')], 1vesforzap = A000004

Links

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

Crossrefs

Cf. A107849, A107850, A107851, A107853.

Programs

Mathematica

CoefficientList[Series[-x(x^2+1)(x+1)^2/((2x^3+x^2-1)(x^4+1)),{x,0, 50}],x] (* or *) LinearRecurrence[ {0,1,2,-1,0,1,2},{0,1,2,3,6,7,10},50] (* Harvey P. Dale, May 03 2024 *)

PARI

a(n)=([0,1,0,0,0,0,0; 0,0,1,0,0,0,0; 0,0,0,1,0,0,0; 0,0,0,0,1,0,0; 0,0,0,0,0,1,0; 0,0,0,0,0,0,1; 2,1,0,-1,2,1,0]^n*[0;1;2;3;6;7;10])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

PARI

concat(0, Vec(x*(1 + x)^2*(1 + x^2) / ((1 - x^2 - 2*x^3)*(1 + x^4)) + O(x^45))) \\ Colin Barker, Apr 30 2019

Formula

a(n) = 2*A159284(n) - A091337(n).

a(n) = a(n-2) + 2*a(n-3) - a(n-4) + a(n-6) + 2*a(n-7) for n>6. - Colin Barker, Apr 30 2019