A107850 Expansion of g.f. (x^2+x+1)*(2*x^2+2*x+1)*(x-1)^2/((1-x^2-2*x^3)*(x^4+1)).

1, 1, 1, 0, 1, 1, 3, 6, 7, 13, 17, 24, 41, 57, 91, 142, 207, 325, 489, 736, 1137, 1713, 2611, 3990, 6039, 9213, 14017, 21288, 32441, 49321, 75019, 114206, 173663, 264245, 402073, 611568, 930561, 1415713, 2153699, 3276838, 4985127, 7584237, 11538801

Offset: 0

Author

Creighton Dement, May 25 2005

Keywords

• easy
• nonn

Comments

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

Links

• Harvey P. Dale, 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, A107851, A107852.

Programs

Mathematica

CoefficientList[Series[(x^2+x+1)(2x^2+2x+1)(x-1)^2/((1-x^2-2x^3)(x^4+1)),{x,0,50}],x] (* or *) LinearRecurrence[{0,1,2,-1,0,1,2},{1,1,1,0,1,1,3},50] (* Harvey P. Dale, Dec 26 2015 *)

Formula

a(n) = A052947(n-1)+A118831(n+6). - R. J. Mathar, Apr 18 2008

a(0)=1, a(1)=1, a(2)=1, a(3)=0, a(4)=1, a(5)=1, a(6)=3, a(n)=a(n-2)+ 2*a(n-3)- a(n-4)+a(n-6)+2*a(n-7). - Harvey P. Dale, Dec 26 2015