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A192417 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (2,2), (3,3). 1
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 (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^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1). - Mark van Hoeij, Apr 17 2013

Conjecture: 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: A150593 A024429 A136412 * A150594 A150595 A150596

Adjacent sequences:  A192414 A192415 A192416 * A192418 A192419 A192420

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jun 30 2011

STATUS

approved

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Last modified June 17 15:07 EDT 2019. Contains 324185 sequences. (Running on oeis4.)