A111574 a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4, with initial terms 1,-1,2,3.

1, -1, 2, 3, 3, 4, 9, 15, 22, 35, 59, 96, 153, 247, 402, 651, 1051, 1700, 2753, 4455, 7206, 11659, 18867, 30528, 49393, 79919, 129314, 209235, 338547, 547780, 886329, 1434111, 2320438, 3754547, 6074987, 9829536, 15904521, 25734055, 41638578, 67372635

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: -4baseiseq[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, A111571, A111572, A111573, A111575, A111576.

Programs

Mathematica

LinearRecurrence[{1,0,1,1},{1,-1,2,3},40] (* Harvey P. Dale, Jan 24 2017 *)

Formula

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

Extensions

Name clarified by Robert C. Lyons, Feb 06 2025