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

Author

Creighton Dement, Apr 08 2009

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A159284, A159285, A159286, A159287.

Programs

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

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 *)

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

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