A149783 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), (-1, 1, 1), (0, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 81, 349, 1555, 6991, 32179, 149207, 697483, 3282551, 15546345, 73935429, 353096835, 1692271669, 8134573751, 39203030799, 189383452871, 916758226553, 4445909748125, 21596830981913, 105068520941583, 511847245118737, 2496580026438073, 12191097513526299, 59592203734144367, 291574621447698169

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[i, 1 + j, k, -1 + n] + aux[1 + 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: A149780 A149781 A149782 * A149784 A240688 A149785

Adjacent sequences: A149780 A149781 A149782 * A149784 A149785 A149786

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved