A149781 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, 0, 0), (0, -1, 1), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 81, 349, 1553, 6971, 32045, 148507, 693999, 3265819, 15462795, 73518369, 351045505, 1682219487, 8085178163, 38961572889, 188203835333, 910988265525, 4417700469303, 21459020639997, 104394577291777, 508550158782913, 2480448375534449, 12112128490415683, 59205372501611963, 289679087093594035

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A346817 A317131 A149780 * A149782 A149783 A149784

Adjacent sequences: A149778 A149779 A149780 * A149782 A149783 A149784

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved