A159288 Expansion of (1 + x + x^2)/(1 - x^2 - 2*x^3).

1, 1, 2, 3, 4, 7, 10, 15, 24, 35, 54, 83, 124, 191, 290, 439, 672, 1019, 1550, 2363, 3588, 5463, 8314, 12639, 19240, 29267, 44518, 67747, 103052, 156783, 238546, 362887, 552112, 839979, 1277886, 1944203, 2957844, 4499975, 6846250, 10415663

Offset

0,3

Comments

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

Starting with offset 1 the sequence appears to be the INVERT transform of (1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, ...). - Gary W. Adamson, Aug 27 2016

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) = A159287(n) + A159287(n+1) + A159287(n+2). - R. J. Mathar, Apr 10 2009

a(n) = a(n-2) + 2*a(n-3) for n>2. - Colin Barker, Apr 29 2019

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

Mathematica

CoefficientList[Series[(1+x+x^2)/(1-x^2-2x^3), {x, 0, 50}], x]  (* Harvey P. Dale, Mar 09 2011 *)
LinearRecurrence[{0, 1, 2}, {1, 1, 2}, 50] (* G. C. Greubel, Jun 27 2018 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, 1, 0]^n*[1; 1; 2])[1, 1] \\ Charles R Greathouse IV, Aug 27 2016
(PARI) Vec((1 + x + x^2) / (1 - x^2 - 2*x^3) + O(x^40)) \\ Colin Barker, Apr 29 2019
(Magma) I:=[1, 1, 2]; [n le 3 select I[n] else Self(n-2) + 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 27 2018

Crossrefs

Cf. A159284, A159285, A159286, A159287.

Sequence in context: A100638 A319437 A270659 * A363958 A033320 A013982

Adjacent sequences: A159285 A159286 A159287 * A159289 A159290 A159291

Keyword

easy,nonn

Author

Creighton Dement, Apr 08 2009

Status

approved