A149862 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, 0), (1, 0, 1)}.

1, 2, 5, 13, 40, 123, 403, 1304, 4497, 15299, 53927, 187356, 675747, 2404640, 8768830, 31561721, 116600798, 425605898, 1582744720, 5818657133, 21820279075, 80958949738, 304934255240, 1136943454365, 4307388239096, 16164654229698, 61432471877142, 231365788916348, 883076005410215, 3341922934503112

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[-1 + i, j, 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: A320809 A287967 A133448 * A149863 A371714 A291614

Adjacent sequences: A149859 A149860 A149861 * A149863 A149864 A149865

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved