|
| |
|
|
A148454
|
|
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, 1, 0), (0, 0, 1), (1, -1, 0), (1, 1, -1)}
|
|
0
| |
|
|
1, 1, 2, 6, 17, 57, 205, 745, 2875, 11305, 45332, 186380, 774303, 3267037, 13949978, 60078464, 261420213, 1145680231, 5056693164, 22468775276, 100367233789, 450802933329, 2034271914025, 9219038987323, 41952247315081, 191591933975581, 878015079137772, 4036487462078620, 18610889183478567
(list; graph; refs; listen; history; internal format)
|
|
|
|
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[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150034 A190915 A032132 * A007743 A000687 A085827
Adjacent sequences: A148451 A148452 A148453 * A148455 A148456 A148457
|
|
|
KEYWORD
| nonn,walk
|
|
|
AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
| |
|
|
