A151322 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), (1,0), (1,1)}.

1, 3, 14, 65, 330, 1683, 8874, 47088, 253802, 1375939, 7524651, 41346061, 228447273, 1267005772, 7054307476, 39394861448, 220641191059, 1238773724011, 6970910527593, 39305772011050, 222039381179593, 1256404002028860, 7120347445063067, 40409910873522737, 229639109317630051, 1306567259328079561

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[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: A026592 A034275 A240008 * A351068 A345683 A002320

Adjacent sequences: A151319 A151320 A151321 * A151323 A151324 A151325

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved