A150745 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), (-1, 1, -1), (1, -1, 0), (1, 0, 1), (1, 1, 1)}.

1, 2, 8, 29, 126, 524, 2387, 10508, 48974, 222544, 1052519, 4878196, 23293729, 109442303, 526219286, 2496617326, 12066173820, 57671916912, 279839865438, 1345193909379, 6548006073396, 31620135178663, 154313964081722, 747937263398326, 3657930720470729, 17783680724340633, 87130717653182968

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[-1 + i, 1 + j, k, -1 + n] + aux[1 + 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: A150742 A150743 A150744 * A150746 A150747 A150748

Adjacent sequences: A150742 A150743 A150744 * A150746 A150747 A150748

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved