A149756 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, 1), (-1, 1, 1), (1, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 5, 17, 85, 329, 1645, 6913, 34565, 152729, 763645, 3482097, 17410485, 81061001, 405305005, 1914744673, 9573723365, 45711939705, 228559698525, 1100105774033, 5500528870165, 26640170717033, 133200853585165, 648290412642625, 3241452063213125, 15838421978898265, 79192109894491325

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A363163 A002020 A038183 * A036756 A149757 A153499

Adjacent sequences: A149753 A149754 A149755 * A149757 A149758 A149759

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved