A148754 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), (-1, 1, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 28, 77, 326, 1028, 4508, 15255, 68726, 244025, 1118063, 4116292, 19085963, 72237186, 337973128, 1307388767, 6159989671, 24254325742, 114924609231, 459192728592, 2185841113614, 8842628338991, 42253748293080, 172757264589725, 828173559499092, 3417317106698596, 16427414281651963

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A148751 A148752 A148753 * A148755 A148756 A352701

Adjacent sequences: A148751 A148752 A148753 * A148755 A148756 A148757

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved