|
| |
|
|
A150969
|
|
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, 0, 0), (0, 1, -1), (1, 0, 1), (1, 1, 1)}
|
|
0
| |
|
|
1, 2, 9, 36, 156, 708, 3242, 15036, 70667, 334535, 1591110, 7611704, 36559791, 176122332, 850932300, 4121606328, 20003197132, 97256045912, 473643889965, 2309916896835, 11279389351186, 55141375665780, 269847701530637, 1321793829895010, 6480105030164733, 31793812875932030, 156104594940769207
(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, -1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A006782 A150968 A073156 * A150970 A150971 A150972
Adjacent sequences: A150966 A150967 A150968 * A150970 A150971 A150972
|
|
|
KEYWORD
| nonn,walk
|
|
|
AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
| |
|
|
