A105225 a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = -1, a(2) = -2.

1, -1, -2, 1, 6, 5, -6, -15, -2, 29, 34, -23, -90, -43, 138, 225, -50, -499, -398, 601, 1398, 197, -2598, -2991, 2206, 8189, 3778, -12599, -20154, 5045, 45354, 35265, -55442, -125971, -15086, 236857, 267030, -206683, -740742, -327375, 1154110, 1808861, -499358, -4117079, -3118362, 5115797

Offset: 0

Author

Creighton Dement, Apr 14 2005

Keywords

• sign
• easy

Comments

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

Links

• Robert Munafo, Sequences Related to Floretions
• Index entries for linear recurrences with constant coefficients, signature (2, -3, 2).

Crossrefs

Cf. A002249, A014551.

Programs

Mathematica

LinearRecurrence[{2,-3,2},{1,-1,-2},50] (* or *) CoefficientList[ Series[ (-3*x^2+3*x-1)/(2*x^3-3*x^2+2*x-1),{x,0,50}],x] (* Harvey P. Dale, Jul 23 2012 *)

Formula

a(n) - a(n+1) = A002249(n).

a(n) = (A002249(n+1) + 1)/2.

From Harvey P. Dale, Jul 23 2012: (Start)

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

a(n)=1/2*(1+(1/2*(1-I*Sqrt[7]))^n+(1/2*(1+I*Sqrt[7]))^n). (End)