A105577 a(n) = 2*a(n-1) - 3*a(n-2) + 2*a(n-3) with a(0) = 1, a(1) = 5, a(2) = 6.

1, 5, 6, -1, -10, -5, 18, 31, -2, -61, -54, 71, 182, 43, -318, -401, 238, 1043, 570, -1513, -2650, 379, 5682, 4927, -6434, -16285, -3414, 29159, 35990, -22325, -94302, -49649, 138958, 238259, -39654, -516169, -436858, 595483, 1469202, 278239, -2660162, -3216637, 2103690, 8536967

Offset: 0

Author

Creighton Dement, Apr 14 2005

Keywords

• sign
• easy

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-3,2).

Crossrefs

Cf. A002249, A014551, A105578.

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

Programs

Mathematica

LinearRecurrence[{2,-3,2},{1,5,6},50] (* Harvey P. Dale, Apr 13 2019 *)

Formula

G.f.: (1+3*x-x^2)/((1-x)*(1-x+2*x^2)). - Colin Barker, Mar 26 2012

E.g.f.: exp(x/2)*(21*exp(x/2) - 7*cos(sqrt(7)*x/2) + 15*sqrt(7)*sin(sqrt(7)*x/2))/14. - Stefano Spezia, May 22 2025