A150244 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, 0, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 6, 22, 84, 334, 1374, 5778, 24688, 106577, 465490, 2050238, 9083750, 40512563, 181633610, 817664224, 3696090185, 16767288215, 76293756214, 348129688283, 1592645474737, 7302821254661, 33555980562246, 154490994132251, 712544695144962, 3291770609667446, 15230615144016301, 70570905651026824

Offset

0,2

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, 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: A121686 A245904 A128723 * A151288 A150245 A150246

Adjacent sequences: A150241 A150242 A150243 * A150245 A150246 A150247

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved