A192417 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (2,2), (3,3).

1, 2, 7, 27, 107, 436, 1810, 7609, 32288, 138009, 593311, 2562725, 11112720, 48347332, 210936119, 922550622, 4043488129, 17755735241, 78099099877, 344033901804, 1517535718392, 6701979806379, 29630948706756, 131136723532257, 580901892464599, 2575423975663301

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1). - Mark van Hoeij, Apr 17 2013

D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +2*(-n+1)*a(n-2) +(-2*n+3)*a(n-3) +(n-2)*a(n-4) +(2*n-5)*a(n-5) +(n-3)*a(n-6)=0. - R. J. Mathar, Oct 08 2016

Mathematica

CoefficientList[Series[1/Sqrt[x^6+2x^5+x^4-2x^3-2x^2-4x+1], {x, 0, 25}], x] (* Michael De Vlieger, Oct 08 2016 *)

Prog

(PARI) /* same as in A092566 but use */
steps=[[0, 1], [1, 0], [2, 2], [3, 3]];
/* Joerg Arndt, Jun 30 2011 */
(PARI) my(x='x+O('x^30)); Vec(1/sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1)) \\ G. C. Greubel, Apr 29 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/Sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1) )); // G. C. Greubel, Apr 29 2019
(Sage) (1/sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 29 2019

Crossrefs

Cf. A001850, A026641, A036355, A137644, A192364, A192365, A192369, A191354.

Sequence in context: A024429 A136412 A360149 * A150594 A150595 A150596

Adjacent sequences: A192414 A192415 A192416 * A192418 A192419 A192420

Keyword

nonn

Author

Joerg Arndt, Jun 30 2011

Status

approved