A159284 Expansion of x*(1+x)/(1-x^2-2*x^3).

0, 1, 1, 1, 3, 3, 5, 9, 11, 19, 29, 41, 67, 99, 149, 233, 347, 531, 813, 1225, 1875, 2851, 4325, 6601, 10027, 15251, 23229, 35305, 53731, 81763, 124341, 189225, 287867, 437907, 666317, 1013641, 1542131, 2346275, 3569413, 5430537

Offset

0,5

Comments

A floretion-generated sequence: 'i + 0.5('ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj')

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Matthias Beck, Neville Robbins, Variations on a Generatingfunctional Theme: Enumerating Compositions with Parts Avoiding an Arithmetic Sequence, arXiv:1403.0665 [math.NT], 2014.

Creighton Dement, Online Floretion Multiplier [broken link]

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3.

Yüksel Soykan, Summing Formulas For Generalized Tribonacci Numbers, arXiv:1910.03490 [math.GM], 2019.

Index entries for linear recurrences with constant coefficients, signature (0,1,2).

Formula

a(n) = abs(A078028(n-1)). - R. J. Mathar, Jul 05 2012

a(n) = a(n-2) + 2*a(n-3), a(0)=0, a(1) = a(2) =1. - G. C. Greubel, Apr 30 2017

a(n) = A052947(n-1)+A052947(n-2). - R. J. Mathar, Mar 23 2023

Mathematica

CoefficientList[Series[x (1+x)/(1-x^2-2x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[ {0, 1, 2}, {0, 1, 1}, 50] (* Harvey P. Dale, Jul 16 2013 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, 1, 0]^n*[0; 1; 1])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016
(Magma) I:=[0, 1, 1]; [n le 3 select I[n] else Self(n-2) + 2*Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 27 2018

Crossrefs

Cf. A159285, A159286, A159287, A159288.

Sequence in context: A072706 A117433 A349054 * A078028 A317142 A279375

Adjacent sequences: A159281 A159282 A159283 * A159285 A159286 A159287

Keyword

easy,nonn

Author

Creighton Dement, Apr 08 2009

Extensions

Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021

Status

approved