A191649 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (1,1), (2,2).

1, 3, 14, 71, 379, 2082, 11651, 66051, 378064, 2180037, 12644861, 73695358, 431209313, 2531556197, 14904832196, 87970766447, 520337606401, 3083584244460, 18304476242735, 108820740004749, 647817646760368, 3861215365595659, 23039691494489015, 137615812845579390

Offset

0,2

Links

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

Formula

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

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

Mathematica

CoefficientList[Series[1/Sqrt[x^4 + 2 x^3 - x^2 - 6 x + 1], {x, 0, 23}], x] (* Michael De Vlieger, Oct 08 2016 *)

Prog

(PARI) /* same as in A092566 but use */
steps=[[0, 1], [1, 0], [1, 1], [2, 2]];
/* Joerg Arndt, Jun 30 2011 */
(PARI) my(x='x+O('x^30)); Vec(1/sqrt(x^4+2*x^3-x^2-6*x+1)) \\ G. C. Greubel, Apr 29 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/Sqrt(x^4+2*x^3-x^2-6*x+1) )); // G. C. Greubel, Apr 29 2019
(Sage) (1/sqrt(x^4+2*x^3-x^2-6*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: A109792 A137177 A158196 * A009637 A098648 A026295

Adjacent sequences: A191646 A191647 A191648 * A191650 A191651 A191652

Keyword

nonn

Author

Joerg Arndt, Jun 30 2011

Status

approved