A111644 Expansion of -(1+x^2)/((x^2+4*x+1)*(x^2-2*x-1)).

1, -6, 29, -124, 501, -1962, 7545, -28696, 108393, -407662, 1528981, -5724500, 21408221, -80003026, 298832369, -1115878064, 4166011601, -15551383382, 58047283725, -216656490156, 808623915973, -3017948390522, 11263433318761, -42036421446600, 156883789264441

Offset: 0

Author

Creighton Dement, Aug 10 2005

Keywords

• easy
• sign

Comments

In reference to the program code, the sequence of Pell numbers A000126 is given by 1kbaseseq[C*J]. A001353 is 1ibaseiseq[C*J].

Floretion Algebra Multiplication Program, FAMP Code: 1basejseq[C*J] with C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' and J = + j' + k' + 1.5'ii' + .5'jj' + .5'kk' + .5e

Links

• Index entries for linear recurrences with constant coefficients, signature (-6,-8,2,1).

Crossrefs

Cf. A111639, A111640, A111641, A111642, A111643, A111645, A000126.

Programs

Mathematica

CoefficientList[Series[-(1+x^2)/((x^2+4x+1)(x^2-2x-1)),{x,0,40}],x] (* or *) LinearRecurrence[{-6,-8,2,1},{1,-6,29,-124},40] (* Harvey P. Dale, May 23 2015 *)

Formula

a(0)=1, a(1)=-6, a(2)=29, a(3)=-124, a(n)=-6*a(n-1)-8*a(n-2)+ 2*a(n-3)+ a(n-4). - Harvey P. Dale, May 23 2015