A151289 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), (1, 1)}

1, 2, 7, 21, 80, 267, 1042, 3655, 14400, 51960, 205770, 756169, 3003754, 11179972, 44496878, 167181919, 666257284, 2521360818, 10057256094, 38278262216, 152783755958, 584199222356, 2332875408218, 8954456162165, 35770374449310, 137743370071244, 550391555936678, 2125263063052980

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[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: A319852 A060900 A305850 * A150300 A150301 A150302

Adjacent sequences: A151286 A151287 A151288 * A151290 A151291 A151292

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved