A150381 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, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 23, 97, 362, 1577, 6240, 28009, 114940, 522955, 2196683, 10100781, 43162414, 199901541, 865225257, 4029080767, 17615868458, 82383872857, 363146829627, 1704094090311, 7562407341100, 35586905917603, 158827126064704, 749146049723839, 3359778029595732, 15878598924571931, 71513032793328165

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, 1 + 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: A150378 A150379 A150380 * A150382 A150383 A150384

Adjacent sequences: A150378 A150379 A150380 * A150382 A150383 A150384

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved