A159285 Expansion of (1+3*x)/(1-x^2-2*x^3).

1, 3, 1, 5, 7, 7, 17, 21, 31, 55, 73, 117, 183, 263, 417, 629, 943, 1463, 2201, 3349, 5127, 7751, 11825, 18005, 27327, 41655, 63337, 96309, 146647, 222983, 339265, 516277, 785231, 1194807, 1817785, 2765269, 4207399, 6400839, 9737937, 14815637

Offset

0,2

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

Creighton Dement, Online Floretion Multiplier [broken link]

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

Formula

a(n) = A052947(n) + 3*A052947(n-1). - R. J. Mathar, Mar 23 2023

Mathematica

LinearRecurrence[{0, 1, 2}, {1, 3, 1}, 50] (* G. C. Greubel, Jun 27 2018 *)
CoefficientList[Series[(1+3x)/(1-x^2-2x^3), {x, 0, 40}], x] (* Harvey P. Dale, Jan 21 2019 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, 1, 0]^n*[1; 3; 1])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016
(Magma) I:=[1, 3, 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. A159284, A159286, A159287, A159288.

Sequence in context: A326729 A171998 A343615 * A021080 A354576 A049764

Adjacent sequences: A159282 A159283 A159284 * A159286 A159287 A159288

Keyword

easy,nonn

Author

Creighton Dement, Apr 08 2009

Status

approved