A149928 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 1), (0, 1, 0), (1, -1, -1), (1, 0, 0)}.

1, 2, 5, 15, 48, 166, 597, 2215, 8510, 33266, 132505, 537363, 2202785, 9140543, 38334918, 162006061, 690358870, 2962720562, 12787564112, 55521222256, 242295294818, 1062048148918, 4675861534171, 20666381911613, 91659316769501, 407917282709291, 1820948836147556, 8151519838832373

Offset

0,2

Links

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

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149927 A035350 A006570 * A003430 A149929 A337262

Adjacent sequences: A149925 A149926 A149927 * A149929 A149930 A149931

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved