A149485 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), (0, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 58, 236, 1061, 4706, 21650, 99606, 466518, 2190098, 10383439, 49367094, 236113304, 1132153966, 5450278252, 26293717423, 127207867136, 616512989395, 2994208483998, 14563343462396, 70948537314877, 346067519427222, 1690198831088196, 8263542216340939, 40443671167837558, 198115841544627367

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, j, -1 + k, -1 + n] + aux[i, 1 + 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: A149482 A149483 A149484 * A006798 A158267 A219572

Adjacent sequences: A149482 A149483 A149484 * A149486 A149487 A149488

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved