A148570 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 6, 19, 52, 177, 572, 2084, 7356, 28195, 105124, 417624, 1619699, 6604938, 26401947, 109851101, 449617572, 1901123505, 7928975462, 33972903518, 143863241757, 623248679117, 2672552178002, 11686567394545, 50642455771423, 223218947010424, 975963035154683, 4331396484379463

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A132335 A148569 A024998 * A148571 A345400 A148572

Adjacent sequences: A148567 A148568 A148569 * A148571 A148572 A148573

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved