A159331 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{1,1} transform (see link).
2, 4, 9, 23, 55, 126, 293, 680, 1581, 3676, 8546, 19867, 46185, 107367, 249598, 580245, 1348906, 3135826, 7289911, 16946987, 39396965, 91586832, 212913553, 494963960, 1150651606, 2674940451, 6218482101, 14456217007, 33606627270
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- R. Choulet, Curtz-like transformation.
- Index entries for linear recurrences with constant coefficients, signature (3,-2,1).
Programs
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Magma
I:=[293, 680, 1581]; [2, 4, 9, 23, 55, 126] 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 26 2018
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Mathematica
Join[{2, 4, 9, 23, 55, 126}, LinearRecurrence[{3, -2, 1}, {293, 680, 1581}, 45]] (* G. C. Greubel, Jun 26 2018 *) -
PARI
z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4+z^6) + (z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 26 2018
Formula
O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4+z^6) + (z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3)).
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 9, with a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=55, a(5)=126, a(6)=293, a(7)=680, a(8)=1581.