A150537 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), (0, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 26, 102, 429, 1830, 8036, 35925, 162302, 743408, 3430182, 15952398, 74673066, 351264524, 1660622930, 7880737509, 37532986236, 179320488307, 859048118661, 4125766305208, 19858333412689, 95775646163821, 462765278447218, 2239646828682571, 10855749266252074, 52691370466962455, 256078519963721463

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, -1 + k, -1 + n] + aux[i, -1 + 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: A326564 A271844 A198957 * A363773 A119243 A264224

Adjacent sequences: A150534 A150535 A150536 * A150538 A150539 A150540

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved