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.

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, 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