A150672 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, 0, -1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 8, 25, 106, 395, 1751, 7102, 32307, 137670, 637149, 2803758, 13133090, 59097808, 279289457, 1277502206, 6078548478, 28151385024, 134670239366, 629777131128, 3025844005173, 14260478538992, 68762414054128, 326128255515484, 1577289458308834, 7520155393725454, 36463648798853574, 174617832362336619

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 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: A122404 A150670 A150671 * A150673 A242747 A195585

Adjacent sequences: A150669 A150670 A150671 * A150673 A150674 A150675

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved