A105579 a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 3, a(2) = 4.

1, 3, 4, 1, -4, -3, 8, 17, 4, -27, -32, 25, 92, 45, -136, -223, 52, 501, 400, -599, -1396, -195, 2600, 2993, -2204, -8187, -3776, 12601, 20156, -5043, -45352, -35263, 55444, 125973, 15088, -236855, -267028, 206685, 740744, 327377, -1154108, -1808859, 499360, 4117081, 3118364, -5115795, -11352520

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..46.

Formula

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

a(n) = 2*a(n-1)-3*a(n-2)+2*a(n-3). G.f.: (1+x+x^2)/((1-x)*(1-x+2*x^2)). [Colin Barker, Mar 27 2012]

Mathematica

Table[(3 - ((1-I*Sqrt[7])^n + (1+I*Sqrt[7])^n)/2^n)/2 // Simplify, {n, 1, 50}] (* Jean-François Alcover, Jun 04 2017 *)

Crossrefs

Cf. A002249, A014551, A078020, A105577, A105578, A105580.

Cf. Equals (1/2) [A107920(n+4) - 2*A107920(n-1) + 3 ].

Sequence in context: A010262 A378038 A201516 * A124446 A293190 A091542

Adjacent sequences: A105576 A105577 A105578 * A105580 A105581 A105582

Keyword

sign,easy

Author

Creighton Dement, Apr 14 2005

Extensions

Corrected by T. D. Noe, Nov 07 2006

Status

approved