|
| |
|
|
A151167
|
|
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, 0)}
|
|
0
| |
|
|
1, 3, 12, 47, 218, 965, 4599, 21221, 102970, 486505, 2382781, 11426421, 56269394, 272411885, 1346576694, 6562913261, 32525351076, 159299916487, 790932819647, 3887965109601, 19330600629450, 95291594229807, 474275668773044, 2343180181071035, 11671642055093232, 57766754545789109, 287925843112694359
(list; graph; refs; listen; history; 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, 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
| Sequence in context: A151164 A151165 A151166 * A064562 A077828 A002001
Adjacent sequences: A151164 A151165 A151166 * A151168 A151169 A151170
|
|
|
KEYWORD
| nonn,walk
|
|
|
AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
| |
|
|
