A159348 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,0} transform (see link).

1, 1, 1, 4, 11, 24, 55, 128, 298, 693, 1611, 3745, 8706, 20239, 47050, 109378, 254273, 591113, 1374171, 3194560, 7426451, 17264404, 40134870, 93302253, 216901423, 504234633, 1172203306, 2725042075, 6334954246, 14726981894, 34236079265

Offset: 0

Author

Richard Choulet, Apr 11 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Richard Choulet, Curtz-like transformation.
• Index entries for linear recurrences with constant coefficients, signature (3,-2,1).

Crossrefs

Cf. A137531, A159347.

Programs

Magma

I:=[11,24,55]; [1,1,1,4] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) +Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 16 2018

Maple

a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=11:a(5):=24:a(6):=55:for n from 4 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);

Mathematica

Join[{1,1,1,4},LinearRecurrence[{3,-2,1},{11,24,55},40]] (* or *) CoefficientList[Series[(-1+2 x-2 x^3+2 x^5-x^6)/(-1+3 x-2 x^2+x^3),{x,0,45}],x](* Harvey P. Dale, Oct 04 2011 *)

PARI

m=50; v=concat([11, 24, 55], vector(m-3)); for(n=4, m, v[n]= 3*v[n-1] -2*v[n-2] +v[n-3]); concat([1,1,1,4], v) \\ G. C. Greubel, Jun 16 2018

Formula

O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4).

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n>=7, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11, a(5)=24, a(6)=55.