A151272 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, 1, 4, 11, 34, 112, 376, 1257, 4330, 15068, 52570, 185086, 657128, 2339972, 8366910, 30070119, 108400594, 391749772, 1420203840, 5161860950, 18797194292, 68593029228, 250803101058, 918497353314, 3368841454202, 12375002551280, 45518663980004, 167631635849400, 618071950062304, 2281410957097608

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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: A243781 A227329 A006765 * A112272 A149234 A149235

Adjacent sequences: A151269 A151270 A151271 * A151273 A151274 A151275

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved