A149446 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), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 4, 13, 48, 174, 664, 2513, 9730, 37582, 147038, 574446, 2260814, 8893738, 35148964, 138890385, 550442708, 2181637152, 8663905570, 34411664264, 136862355144, 544428822504, 2167767306078, 8633032307046, 34404130526250, 137130510324094, 546859386049220, 2181154062631162

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, 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: A351509 A149444 A149445 * A149447 A357642 A149448

Adjacent sequences: A149443 A149444 A149445 * A149447 A149448 A149449

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved