|
|
A151211
|
|
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, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 1)}
|
|
0
|
|
|
1, 3, 13, 53, 251, 1123, 5443, 25319, 124085, 589525, 2907101, 13992377, 69260281, 336246069, 1668515057, 8149453349, 40508704195, 198730129755, 989055732315, 4868337933007, 24251331823247, 119677240767379, 596579249085239, 2950013134883235, 14713426845193475, 72874410714058567, 363620465475437771
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
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, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + 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
|
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|