A151327 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, -1), (1, 0), (1, 1)}.

1, 3, 15, 76, 413, 2281, 12889, 73541, 423921, 2458383, 14335834, 83922633, 492956132, 2903156720, 17135951352, 101330250964, 600140389918, 3559105598556, 21131319068601, 125585737386758, 747013179830622, 4446753991483192, 26487831271866795, 157871848076357815, 941434100552046728

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..400

A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.

M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.

Maple

F:= proc(x, y, n) option remember; local t, s, u;
     t:= 0:
     if n <= min(x, y) then return 6^n fi;
     for s in [[-1, 1], [-1, 0], [0, 1], [1, -1], [1, 0], [1, 1]] do
       u:= [x, y]+s;
       if min(u) >= 0 then t:= t + procname(op(u), n-1) fi
     od;
     t
end proc:
seq(F(0, 0, n), n=0..40); # Robert Israel, Jun 05 2018

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A037647 A019477 A019478 * A037766 A037654 A074561

Adjacent sequences: A151324 A151325 A151326 * A151328 A151329 A151330

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved