A151277 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, 1), (-1, 0), (0, -1), (1, -1), (1, 1)}

1, 1, 6, 19, 92, 380, 1858, 8531, 42322, 205486, 1036242, 5197028, 26600656, 136247450, 706258300, 3671453391, 19233967034, 101105026444, 534364343102, 2833591923458, 15087564248648, 80576221523390, 431730827926256, 2319409832695016, 12494373170976880, 67463786953484884, 365108831177564780

Offset

0,3

Links

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

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

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

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, -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: A041937 A279512 A111510 * A192368 A355539 A323686

Adjacent sequences: A151274 A151275 A151276 * A151278 A151279 A151280

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved