A149076 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, 1, 4, 7, 28, 62, 258, 669, 2872, 8202, 35902, 109484, 486544, 1558474, 7007624, 23310931, 105792634, 362683186, 1658516164, 5827726534, 26818213980, 96192530864, 445026604190, 1624336763598, 7549247734720, 27971272771960, 130514411695862, 489935655695282, 2293982541556926

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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: A128386 A149074 A149075 * A123767 A149077 A149078

Adjacent sequences: A149073 A149074 A149075 * A149077 A149078 A149079

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved