A149631 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), (-1, 0, 1), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 15, 67, 265, 1181, 5057, 23041, 102333, 474523, 2156643, 10120107, 46736465, 221204517, 1033504091, 4923295415, 23207349767, 111106803733, 527407044525, 2535136109557, 12101424510769, 58362499485643, 279860547706107, 1353507920535397, 6514735121670749, 31583796575639321, 152498848752023229

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] + 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: A149628 A149629 A149630 * A079569 A149632 A149633

Adjacent sequences: A149628 A149629 A149630 * A149632 A149633 A149634

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved