A111571 a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4, with initial terms 1,1,-2,-1.

1, 1, -2, -1, 1, 0, -3, -3, -2, -5, -11, -16, -23, -39, -66, -105, -167, -272, -443, -715, -1154, -1869, -3027, -4896, -7919, -12815, -20738, -33553, -54287, -87840, -142131, -229971, -372098, -602069, -974171, -1576240, -2550407, -4126647, -6677058, -10803705

Offset: 0

Author

Creighton Dement, Aug 10 2005

Keywords

• easy
• sign

Comments

See comment and FAMP code for A111569.

Floretion Algebra Multiplication Program, FAMP Code: 1jesseq[B+H] with B = - .25'i + .25'j - .25i' + .25j' + k' - .5'kk' - .25'ik' - .25'jk' - .25'ki' - .25'kj' - .5e and H = + .75'ii' + .75'jj' + .75'kk' + .75e

Links

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

Crossrefs

Cf. A001638, A111569, A111570, A111572, A111573, A007598, A000045.

Programs

Mathematica

LinearRecurrence[{1,0,1,1},{1,1,-2,-1},40] (* or *) CoefficientList[ Series[ (-1+3*x^2)/((1+x^2)*(x^2+x-1)),{x,0,40}],x]  (* Harvey P. Dale, Apr 23 2011 *)

Formula

G.f.: (-1+3*x^2)/((1+x^2)*(x^2+x-1)).

Extensions

Name clarified by Robert C. Lyons, Feb 06 2025