A105578 a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 1, a(2) = 0.

1, 1, 0, -1, 0, 3, 4, -1, -8, -5, 12, 23, 0, -45, -44, 47, 136, 43, -228, -313, 144, 771, 484, -1057, -2024, 91, 4140, 3959, -4320, -12237, -3596, 20879, 28072, -13685, -69828, -42457, 97200, 182115, -12284, -376513, -351944, 401083, 1104972, 302807, -1907136, -2512749, 1301524, 6327023, 3723976

Offset: 0

Author

Creighton Dement, Apr 14 2005

Keywords

• sign
• easy

Comments

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

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-3,2).

Crossrefs

Cf. A002249, A014551, A078020, A105577, A105579.

Equals (A107920(n) + 1)/2.

Programs

Mathematica

-Join[{-1,-1,a=0,b=1},Table[c=1*b-2*a-1;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 21 2011 *)
LinearRecurrence[{2,-3,2},{1,1,0},50] (* Harvey P. Dale, Mar 28 2019 *)

PARI

Vec(-(x^2-x+1)/((x-1)*(2*x^2-x+1)) + O(x^100)) \\ Colin Barker, Feb 08 2015

Formula

a(n) - a(n+1) = A001607(n); a(n+2) - 2a(n+1) + a(n) = - A078020(n).

G.f.: -(x^2-x+1) / ((x-1)*(2*x^2-x+1)). - Colin Barker, Feb 08 2015