A151257 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, 1, 2, 4, 11, 26, 70, 195, 558, 1578, 4678, 14067, 42248, 128588, 399183, 1241119, 3873090, 12243222, 38947570, 124009672, 397559401, 1283652201, 4152226324, 13472767649, 43967385684, 143918657309, 471891799395, 1553179013035, 5129597538276, 16968589795201, 56263344975599, 187121094027032

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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: A080009 A159336 A240571 * A148117 A148118 A148119

Adjacent sequences: A151254 A151255 A151256 * A151258 A151259 A151260

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved