A151293 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, 1)}.

1, 2, 7, 24, 88, 328, 1246, 4779, 18485, 71918, 281102, 1102653, 4337842, 17104951, 67577658, 267410057, 1059581561, 4203221319, 16689714274, 66324649355, 263761185264, 1049579758069, 4178825351781, 16645543692333, 66331807758634, 264426232745902, 1054454512710944, 4206064951123326

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, 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: A270490 A104625 A221454 * A122446 A150390 A052705

Adjacent sequences: A151290 A151291 A151292 * A151294 A151295 A151296

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved