A149636 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, 0, 1), (-1, 1, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 69, 233, 1123, 4193, 20445, 79657, 391523, 1581335, 7802551, 32250205, 159611321, 671656495, 3331359929, 14211713979, 70601547625, 304539943445, 1514683890949, 6593142774295, 32821605294277, 143954466315923, 717132984141773, 3165624935768595, 15779028426737607, 70039409190070017

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, k, -1 + n] + aux[1 + i, 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: A149633 A149634 A149635 * A149637 A149638 A149639

Adjacent sequences: A149633 A149634 A149635 * A149637 A149638 A149639

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved