A149707 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, 0), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 69, 293, 1265, 5491, 24899, 112365, 512129, 2375379, 11021119, 51362551, 241955331, 1140089861, 5389039923, 25643375625, 122089489367, 582545550925, 2792190962759, 13390874237149, 64325964827093, 309993813229519, 1494740037908429, 7216598973065037, 34923885056860867, 169100310595959259

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149705 A149706 A273763 * A214003 A249015 A273852

Adjacent sequences: A149704 A149705 A149706 * A149708 A149709 A149710

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved