A151097 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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 3, 11, 43, 180, 774, 3431, 15428, 70548, 325431, 1516925, 7112596, 33584632, 159251552, 758919860, 3628089772, 17408822079, 83737680086, 403929643759, 1952239163441, 9456497683517, 45878748056839, 222983221783390, 1085170262087486, 5288848011083883, 25804657251783199, 126056290017227100

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A149072 A284720 A151096 * A151098 A277220 A338999

Adjacent sequences: A151094 A151095 A151096 * A151098 A151099 A151100

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved