|
Search: id:A148473
|
|
|
| A148473 |
|
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, 0, 0), (-1, 0, 1), (0, -1, 0), (0, 0, 1), (1, 1, -1)} |
|
+0
1
|
|
| 1, 1, 2, 6, 20, 65, 226, 838, 3201, 12386, 48948, 197608, 809096, 3345155, 13980334, 59041103, 251334992, 1076995274, 4645807488, 20164588874, 87973297367, 385580488738, 1697545399851, 7504250584691, 33293669209338, 148208341418642, 661867001127396, 2964446051683526, 13313133410772356
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A052958 A053730 A005726 this_sequence A000718 A148474 A156831
Adjacent sequences: A148470 A148471 A148472 this_sequence A148474 A148475 A148476
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
|
|
Search completed in 0.002 seconds
|
