A150322 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, 1), (-1, 0, 0), (0, 0, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 22, 85, 314, 1277, 5137, 21608, 91278, 393985, 1714919, 7555790, 33553007, 150242961, 677010989, 3070101991, 13992710552, 64093411496, 294810790148, 1361431299491, 6309350784520, 29334883095221, 136799486813059, 639698512842728, 2998957058785102, 14092532738798394, 66367576376616777

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[i, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A007867 A241156 A014558 * A150323 A150324 A150325

Adjacent sequences: A150319 A150320 A150321 * A150323 A150324 A150325

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved