A149642 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), (0, 1, -1), (1, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 71, 239, 1163, 4345, 21417, 83977, 416265, 1686337, 8383997, 34790589, 173269929, 731926875, 3649321671, 15627492163, 77977391863, 337568268171, 1685309454471, 7360687552519, 36762621786387, 161749719323503, 808077816764431, 3577616979975647, 17876871296933983, 79569969818904111

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, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A355507 A259205 A149641 * A149643 A149644 A149645

Adjacent sequences: A149639 A149640 A149641 * A149643 A149644 A149645

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved