A150195 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), (0, 0, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 6, 21, 79, 304, 1223, 5028, 21047, 89251, 383518, 1663928, 7276480, 32045842, 142037287, 632872830, 2832858397, 12734620947, 57464148718, 260162526888, 1181426526600, 5380086708793, 24562294842043, 112393730436929, 515397881372591, 2368117618280042, 10900588201137940, 50260446215458211

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, j, k, -1 + n] + aux[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, 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: A306832 A121941 A150194 * A363810 A150196 A366082

Adjacent sequences: A150192 A150193 A150194 * A150196 A150197 A150198

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved