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A159330 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,1} transformation (see link). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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.

MATHEMATICA

Join[{2, 4, 9, 23}, LinearRecurrence[{3, -2, 1}, {55, 126, 292}, 47]] (* G. C. Greubel, Jun 26 2018 *)

PROG

(PARI) z='z+O('z^30); 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

(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

CROSSREFS

Cf. A159328, A159329.

Sequence in context: A278691 A159329 A159334 * A159331 A135346 A174283

Adjacent sequences:  A159327 A159328 A159329 * A159331 A159332 A159333

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 10 2009

STATUS

approved

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Last modified December 12 19:33 EST 2018. Contains 318081 sequences. (Running on oeis4.)