A149790 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, 0, 1), (-1, 1, 1), (0, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 83, 359, 1625, 7371, 34221, 159265, 750635, 3549039, 16901211, 80719115, 387326417, 1862934899, 8989681705, 43464846179, 210653684411, 1022600084099, 4973156298249, 24218455299305, 118108990015125, 576652082980411, 2818691479922419, 13791157832630847, 67541251407602393

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A094726 A149788 A149789 * A017963 A149791 A149792

Adjacent sequences: A149787 A149788 A149789 * A149791 A149792 A149793

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved