A150976 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, 0), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 36, 168, 737, 3582, 16548, 81032, 382762, 1890435, 9071907, 44923827, 217534842, 1080563215, 5269297335, 26206186223, 128382787217, 639395569356, 3144154838613, 15669351408709, 77258894907688, 385315579777762, 1904096710220571, 9500036064922626, 47025429577566991, 234722271569474468

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, -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, 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: A248438 A288780 A150975 * A150977 A150978 A121345

Adjacent sequences: A150973 A150974 A150975 * A150977 A150978 A150979

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved