A151300 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, 0), (1, -1), (1, 0), (1, 1)}.

1, 2, 8, 28, 118, 469, 2039, 8559, 37909, 164062, 735698, 3246436, 14688132, 65690534, 299227510, 1351439955, 6188946223, 28161550486, 129528141204, 592866204918, 2736746791312, 12585998174974, 58276845530802, 269058921980442, 1249107763866352, 5785962784369466, 26923056650212598, 125058263384130622

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, 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: A150718 A344558 A217720 * A150719 A150720 A150721

Adjacent sequences: A151297 A151298 A151299 * A151301 A151302 A151303

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved