A150365 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, 0, 1), (1, 0, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 23, 93, 356, 1533, 6323, 28181, 121468, 553175, 2454032, 11342113, 51341090, 239851262, 1101887943, 5189868066, 24112416255, 114298452653, 535738501325, 2552659959623, 12049599738188, 57657545055704, 273741321615889, 1314519545306737, 6270891851673588, 30204155178887175, 144669427270233651

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150363 A150364 A093636 * A150366 A150367 A150368

Adjacent sequences: A150362 A150363 A150364 * A150366 A150367 A150368

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved