A111645 Expansion of (x+1)*(1-3*x)/((x^2+4*x+1)*(x^2-2*x-1)).

-1, 8, -37, 156, -625, 2436, -9341, 35464, -133809, 502896, -1885317, 7056580, -26384961, 98589388, -368228797, 1374944336, -5133041825, 19160828056, -71518973861, 266936079404, -996276071249, 3718290672596, -13877182280637, 51791152239960, -193289149920721

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: 1jbasejseq[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, A111644, A000126.

Programs

Mathematica

CoefficientList[Series[(x+1)(1-3x)/((x^2+4x+1)(x^2-2x-1)),{x,0,30}],x] (* or *) LinearRecurrence[{-6,-8,2,1},{-1,8,-37,156},30] (* Harvey P. Dale, Nov 19 2015 *)

Formula

a(0)=-1, a(1)=8, a(2)=-37, a(3)=156, a(n)=-6*a(n-1)-8*a(n-2)+2*a(n-3)+a(n-4). - Harvey P. Dale, Nov 19 2015

2*a(n) = -7*A125905(n)-A125905(n-1) -A077985(n-1)+5*A077985(n). - R. J. Mathar, Sep 11 2019