A149542 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, 1, -1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 53, 181, 797, 2903, 13207, 51113, 237309, 949867, 4447019, 18266547, 86272555, 360467707, 1716329559, 7273137801, 34833761525, 149321208635, 718010320583, 3106869092833, 14994243295209, 65380081591941, 316582059936937, 1389603461763933, 6746389645694401, 29784612663768153

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A328494 A149540 A149541 * A089794 A216821 A039510

Adjacent sequences: A149539 A149540 A149541 * A149543 A149544 A149545

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved