A150841 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, 0), (0, -1, 0), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 32, 138, 612, 2764, 12700, 58968, 276528, 1305745, 6201839, 29599678, 141827398, 681967982, 3288696968, 15900565194, 77048864705, 374090158891, 1819483169075, 8863255852580, 43236468163514, 211179733453264, 1032648061022020, 5054786347652530, 24766533837228243, 121452184499118348

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150838 A150839 A150840 * A150842 A274483 A308152

Adjacent sequences: A150838 A150839 A150840 * A150842 A150843 A150844

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved