A159334 Transform of A056594 by the T_{1,1} transformation (see link)

2, 4, 9, 23, 55, 126, 291, 678, 1578, 3667, 8523, 19815, 46066, 107089, 248950, 578740, 1345409, 3127695, 7271007, 16903042, 39294807, 91349342, 212361454, 493680487, 1147667895, 2668004163, 6202357186, 14418731129, 33519483178

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,-3,4,-2,1).

Formula

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

for n>=0 a(n+5)=3*a(n+4)-3*a(n+3)+4*a(n+2)-2*a(n+1)+a(n)

Mathematica

Join[{2, 4, 9, 23, 55, 126}, LinearRecurrence[{3, -3, 4, -2, 1}, {291, 678, 1578, 3667, 8523}, 45]] (* G. C. Greubel, Jun 25 2018 *)

Prog

(PARI) x='x+O('x^50); Vec(-(2-2*x+3*x^2+x^4)/((x^2+1)*(x^3-2*x^2+3*x-1))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[291, 678, 1578, 3667, 8523]; [2, 4, 9, 23, 55, 126] cat [n le 5 select I[n] else 3*Self(n-1) - 3*Self(n-2) + 4*Self(n-3) -2*Self(n-4) +Self(n-5): n in [1..50]]; // G. C. Greubel, Jun 25 2018

Crossrefs

Cf. A159328, A159329, A159330, A159331.

Sequence in context: A292790 A278691 A159329 * A159330 A159331 A135346

Adjacent sequences: A159331 A159332 A159333 * A159335 A159336 A159337

Keyword

easy,nonn

Author

Richard Choulet, Apr 10 2009

Status

approved