A151467 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), (1, 0), (1, 1)}.

1, 0, 5, 5, 60, 143, 1026, 3666, 21645, 94376, 518078, 2496709, 13395620, 68061470, 364081314, 1906396512, 10243047235, 54647381651, 295593657670, 1597150643075, 8699338664954, 47443092772573, 260081606235808, 1428683475568373, 7876997150310977, 43524929450676109, 241181417275425104

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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

Crossrefs

Sequence in context: A368894 A009390 A009334 * A241209 A171726 A129358

Adjacent sequences: A151464 A151465 A151466 * A151468 A151469 A151470

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved