A151001 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), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 38, 175, 808, 3849, 18383, 88999, 431862, 2110755, 10334433, 50809851, 250155363, 1234791555, 6101767949, 30203112734, 149633428158, 742180468673, 3683782579592, 18299486557614, 90954995144055, 452356538672065, 2250765627720072, 11204242622439625, 55794642239484282, 277945913282431755

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, -1 + 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, 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: A150998 A150999 A151000 * A151002 A151003 A357547

Adjacent sequences: A150998 A150999 A151000 * A151002 A151003 A151004

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved