A159350 Transform of A056594 by the T_{0,0} transformation (see link).

1, 1, 1, 4, 11, 24, 54, 127, 297, 689, 1600, 3721, 8652, 20112, 46753, 108689, 252673, 587392, 1365519, 3174448, 7379698, 17155715, 39882197, 92714861, 215535904, 501060185, 1164823608, 2707886360, 6295072049, 14634267033, 34020543361

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..2700

Richard Choulet, Curtz-like transformation.

Index entries for linear recurrences with constant coefficients, signature (3,-3,4,-2,1).

Formula

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

a(n) = 3*a(n-1) - 3*a(n-2) + 4*a(n-3) - 2*a(n-4) + a(n-5) for n >= 5, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11.

Maple

a(0):=1: a(1):=1: a(2):=1: a(3):=4: a(4):=11: for n from 0 to 31 do a(n+5):=3*a(n+4)-3*a(n+3)+4*a(n+2)-2*a(n+1)+a(n): od: seq(a(i), i=0..31);

Mathematica

LinearRecurrence[{3, -3, 4, -2, 1}, {1, 1, 1, 4, 11}, 50] (* G. C. Greubel, Jun 15 2018 *)

Prog

(PARI) x='x+O('x^50); Vec((1-x)^2/((1-3*x+2*x^2-x^3)*(1+x^2))) \\ G. C. Greubel, Jun 15 2018
(Magma) I:=[1, 1, 1, 4, 11]; [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 15 2018

Crossrefs

Cf. A137531, A159347, A159348, A159349.

Sequence in context: A007678 A339493 A364282 * A159348 A159349 A349569

Adjacent sequences: A159347 A159348 A159349 * A159351 A159352 A159353

Keyword

easy,nonn

Author

Richard Choulet, Apr 11 2009

Status

approved