A149173 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, 1), (-1, 0, 0), (0, -1, 0), (0, 1, -1), (1, 1, 0)}.

1, 1, 4, 10, 34, 116, 414, 1520, 5801, 22425, 88356, 354015, 1436161, 5883984, 24364534, 101756744, 428049139, 1812818242, 7726376444, 33107102100, 142560071609, 616726081964, 2679247585672, 11683377518921, 51128959743600, 224495464642072, 988696444896896, 4366576279940710, 19336461231673449

Offset

0,3

Links

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

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, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A231524 A182645 A006343 * A149174 A283070 A222631

Adjacent sequences: A149170 A149171 A149172 * A149174 A149175 A149176

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved