A159330 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,1} transformation (see link).
2, 4, 9, 23, 55, 126, 292, 679, 1579, 3671, 8534, 19839, 46120, 107216, 249247, 579429, 1347009, 3131416, 7279659, 16923154, 39341560, 91458031, 212614127, 494267879, 1149033414, 2671178611, 6209736884, 14435886844, 33559365375, 78016059321, 181365334057
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
-
Magma
I:=[55, 126, 292]; [2, 4, 9, 23] 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
-
Mathematica
Join[{2, 4, 9, 23}, LinearRecurrence[{3, -2, 1}, {55, 126, 292}, 47]] (* G. C. Greubel, Jun 26 2018 *) -
PARI
my(z='z+O('z^31)); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4) + 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/(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 >= 7, with a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=55, a(5)=126, a(6)=292.