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.

Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008.

Mireille Bousquet-Mélou and Marni Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008.

Marni Mishna and Juan Pulido, On the small-step quarter plane lattice walks with a non D-finite univariate generating function, arXiv:2605.16688 [math.CO], 2026. See p. 12 (Table 5).

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