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A191649 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (1,1), (2,2). 1
1, 3, 14, 71, 379, 2082, 11651, 66051, 378064, 2180037, 12644861, 73695358, 431209313, 2531556197, 14904832196, 87970766447, 520337606401, 3083584244460, 18304476242735, 108820740004749, 647817646760368, 3861215365595659, 23039691494489015, 137615812845579390 (list; graph; refs; listen; history; text; internal format)
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: 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,changed

AUTHOR

Joerg Arndt, Jun 30 2011

STATUS

approved

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Last modified January 21 11:11 EST 2020. Contains 331105 sequences. (Running on oeis4.)