A151463 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1)}.

1, 1, 2, 5, 15, 44, 150, 508, 1846, 6764, 25858, 99709, 395433, 1582181, 6453404, 26545529, 110719053, 465350515, 1976488255, 8452069209, 36442285744, 158070027834, 690215772176, 3029731896605, 13372814816821, 59299189416860, 264184060358888, 1181773176878004, 5307755174138710

Offset

0,3

Links

Table of n, a(n) for n=0..28.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

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[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[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A220873 A148351 A148352 * A148353 A336417 A232208

Adjacent sequences: A151460 A151461 A151462 * A151464 A151465 A151466

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved