A224508 a(n+2) = a(n+1) + a(n) + A*t^n, with A = 1 and t = -2.

0, 1, 2, 1, 7, 0, 23, -9, 78, -59, 275, -296, 1003, -1341, 3758, -5775, 14367, -24176, 55727, -99521, 218350, -405459, 861467, -1641144, 3414627, -6615125, 13576718, -26592839, 54092743, -106717824, 215810375, -427778361, 861773838, -1713488171, 3443252963

Offset

0,3

Comments

With these particular values, a(n) turns out to be Fibonacci(n) + (-2)^n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

C. N. Phadte and S. P. Pethe, On second order non homogeneous recurrence relation, Annales Mathematicae et Infomaticae, 41 (2013), 205-210.

Index entries for linear recurrences with constant coefficients, signature (-1,3,2).

Formula

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

Mathematica

nn = 40; A = 1; t = -2; CoefficientList[Series[(x + x^2 (A - t))/((1 - x*t) (1 - x - x^2)), {x, 0, nn}], x] (* T. D. Noe, Sep 21 2013 *) (* or *)
LinearRecurrence[{-1, 3, 2}, {0, 1, 2}, 35] (* Georg Fischer, Jan 26 2022 *)

Crossrefs

Cf. A227200.

Sequence in context: A051258 A063704 A224918 * A360894 A116891 A079620

Adjacent sequences: A224505 A224506 A224507 * A224509 A224510 A224511

Keyword

sign,easy

Author

Chandrakant N Phadte and Yeshwant Shivrai Valaulikar, Sep 18 2013

Status

approved