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).

1, 3, 22, 165, 1327, 10950, 92045, 783579, 6733966, 58294401, 507579829, 4440544722, 39000863629, 343677908223, 3037104558574, 26904952725061, 238854984979423, 2124492829796598, 18927927904130617, 168888613467092895, 1508973226894216106, 13498652154574126523, 120886709687492946083

Offset

0,2

Links

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

Formula

G.f.: sqrt( ((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-François 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 from Joerg Arndt, Jun 30 2011

Status

approved