A104770 Expansion of g.f. (1+x^2)/(1+x-x^3).

1, -1, 2, -1, 0, 2, -3, 3, -1, -2, 5, -6, 4, 1, -7, 11, -10, 3, 8, -18, 21, -13, -5, 26, -39, 34, -8, -31, 65, -73, 42, 23, -96, 138, -115, 19, 119, -234, 253, -134, -100, 353, -487, 387, -34, -453, 840, -874, 421, 419, -1293, 1714, -1295, 2, 1712, -3007, 3009, -1297, -1710, 4719, -6016

Offset: 0

Author

Creighton Dement, Mar 24 2005

Keywords

• sign
• easy

Comments

A floretion-generated sequence.

Floretion Algebra Multiplication Program, FAMP Code: Define A = + .5'i + .5'j + .5'k + .5e and B = + .5'i + .5i' + .5'ii' + .5e. Then (a(n)) = jesloop(infty)-jesleftfor[A*B], ForType: 1A.

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,0,1).

Crossrefs

Cf. A104769, A104771.

Programs

Mathematica

CoefficientList[Series[(1+x^2)/(1+x-x^3),{x,0,60}],x] (* or *) LinearRecurrence[ {-1,0,1},{1,-1,2},70] (* Harvey P. Dale, Jan 27 2013 *)

Formula

Recurrence: a(n+3) = a(n) - a(n+2); a(0) = 1, a(1) = -1, a(2) = 2.

a(n+1) - a(n) = ((-1)^(n+1))*a(n+5); a(n) = A104771(n) - A104769(n).

a(n+1) = -(A104769(n) + A104769(n+2)), n>=0. - Ralf Stephan, Apr 05 2009

Extensions

Edited by Ralf Stephan, Apr 05 2009