A151258 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), (0, 1), (1, -1)}

1, 1, 2, 4, 12, 28, 86, 228, 736, 2070, 6868, 20212, 68300, 207620, 711694, 2217096, 7683384, 24405062, 85318256, 275290932, 969323508, 3168559356, 11223800316, 37092325140, 132060026316, 440527174396, 1575294513724, 5297495810812, 19015832114996, 64400390557052, 231947048982446, 790430109713200

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, -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: A096581 A275434 A364316 * A148175 A148176 A148177

Adjacent sequences: A151255 A151256 A151257 * A151259 A151260 A151261

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved