A149662 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, -1, 0), (0, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 61, 241, 995, 4061, 16877, 71739, 308905, 1330317, 5777979, 25333477, 111749727, 493731117, 2191906317, 9780182467, 43796700389, 196437535731, 883766969625, 3988570831623, 18044717963917, 81747470960801, 371126227282463, 1688513030862509, 7695691223929163, 35114479996825881

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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A273503 A273680 A273759 * A149663 A149664 A149665

Adjacent sequences: A149659 A149660 A149661 * A149663 A149664 A149665

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved