A151303 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (1, -1), (1, 0), (1, 1)}

1, 2, 8, 30, 122, 508, 2163, 9336, 40804, 179887, 799120, 3571698, 16048114, 72428799, 328167457, 1491978164, 6803716892, 31110321096, 142600055057, 655074921487, 3015313208782, 13904953770666, 64229950295692, 297152727581176, 1376720785809034, 6386921652633456, 29667247964299526, 137964512850757605

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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

Crossrefs

Sequence in context: A150759 A150760 A230588 * A150761 A373176 A150762

Adjacent sequences: A151300 A151301 A151302 * A151304 A151305 A151306

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved