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A192365 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(2,0),(0,1),(0,2),(1,1),(2,2). 8
1, 3, 22, 165, 1327, 10950, 92045, 783579, 6733966, 58294401, 507579829, 4440544722, 39000863629, 343677908223, 3037104558574, 26904952725061, 238854984979423, 2124492829796598, 18927927904130617, 168888613467092895, 1508973226894216106, 13498652154574126523, 120886709687492946083 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.:  ogf^2 = ((2*x^2+6*x-3)/p4 - 2/sqrt(p4))/(4*x^2-4*x-5) where p4 = x^4+6*x^3+7*x^2-10*x+1. - Mark van Hoeij, Apr 16 2013

MAPLE

p4 := x^4+6*x^3+7*x^2-10*x+1;

ogf := sqrt( ((2*x^2+6*x-3)/p4 - 2/sqrt(p4))/(4*x^2-4*x-5) );

series(ogf, x=0, 30);  # Mark van Hoeij, Apr 16 2013

# second Maple program:

b:= proc(x, y) option remember; `if`(min(x, y)<0, 0,

      `if`(max(x, y)=0, 1, add(b(x, y-j)+

         b(x-j, y)+b(x-j, y-j), j=1..2)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);  # Alois P. Heinz, May 16 2017

MATHEMATICA

b[x_, y_] := b[x, y] = If[Min[x, y] < 0, 0, If[Max[x, y] == 0, 1, Sum[b[x, y - j] + b[x - j, y] + b[x - j, y - j], {j, 1, 2}]]];

a[n_] := b[n, n];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jun 23 2017, after Alois P. Heinz *)

PROG

(PARI) /* same as in A092566 but use */

steps=[[0, 1], [0, 2], [1, 0], [2, 0], [1, 1], [2, 2]];

/* Joerg Arndt, Jun 30 2011 */

CROSSREFS

Sequence in context: A183259 A218668 A164021 * A074578 A290719 A074576

Adjacent sequences:  A192362 A192363 A192364 * A192366 A192367 A192368

KEYWORD

nonn

AUTHOR

Eric Werley, Jun 29 2011

EXTENSIONS

Terms >507579829 by Joerg Arndt, Jun 30 2011.

STATUS

approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)