A149190 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, 1, -1), (-1, 1, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 10, 37, 131, 463, 1791, 6833, 26461, 105324, 418000, 1684410, 6836168, 27822562, 114359718, 471222489, 1949627785, 8111429509, 33814239567, 141474465630, 593788937120, 2497289823470, 10532283248988, 44511268227061, 188474107078536, 799722370589753, 3398695398963970

Offset

0,3

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A025237 A149188 A149189 * A102755 A197551 A046562

Adjacent sequences: A149187 A149188 A149189 * A149191 A149192 A149193

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved