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

Author

Richard Choulet, Apr 10 2009

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A159328, A159329, A159330, A159331.

Programs

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

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 *)

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

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)