A150728 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, 0), (0, 1, -1), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 8, 28, 126, 524, 2356, 10660, 48830, 226132, 1061284, 4986156, 23637740, 112621728, 537913296, 2580704988, 12424532670, 59913275180, 289768069756, 1404617870656, 6817531259968, 33155761222168, 161507474835304, 787520829969380, 3845498249516300, 18800150173178792, 91985427350888920

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A150725 A150726 A150727 * A150729 A075662 A150730

Adjacent sequences: A150725 A150726 A150727 * A150729 A150730 A150731

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved