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

Author

Creighton Dement, Apr 08 2009

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A159284, A159286, A159287, A159288.

Programs

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

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 *)

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

Formula

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