A151309 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, 2, 9, 35, 160, 720, 3413, 16220, 78941, 386168, 1913966, 9534469, 47882879, 241540800, 1225176455, 6237701908, 31886453967, 163506199839, 841042932257, 4337370857108, 22424551961962, 116189867455606, 603271009373456, 3138073094395283, 16352089769050877, 85344855526327286, 446101304547583159

Offset

0,2

Links

Table of n, a(n) for n=0..26.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

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, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A150954 A150955 A150956 * A150957 A150958 A150959

Adjacent sequences: A151306 A151307 A151308 * A151310 A151311 A151312

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved