A131041 a(n) = 2*a(n-1) - a(n-2) - a(n-4).

1, 1, 1, -1, -4, -8, -13, -17, -17, -9, 12, 50, 105, 169, 221, 223, 120, -152, -645, -1361, -2197, -2881, -2920, -1598, 1921, 8321, 17641, 28559, 37556, 38232, 21267, -24257, -107337, -228649, -371228, -489550, -500535, -282871, 306021

Offset: 0

Author

Creighton Dement, Jun 11 2007

Keywords

• easy
• sign

Comments

Generating floretion is .5i' + .5j' + .5k' + .5e + 'ii' (for A131039 it is 'i + .5i' + .5j' + .5k' + .5e and for A131040 it is 1.5i' + .5j' + .5k' + .5e)

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, -1).

Crossrefs

Cf. A131039, A131040, A131042, A002316, A002531.

Programs

Maple

Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[.5i' + .5j' + .5k' + .5e + 'ii']

Mathematica

LinearRecurrence[{2,-1,0,-1},{1,1,1,-1},40] (* Harvey P. Dale, Oct 14 2012 *)

Formula

G.f. (1-x-2*x^3)/(1-2*x+x^2+x^4)