|
Search: id:A148085
|
|
|
| A148085 |
|
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, 1), (-1, 0, 1), (0, 1, -1), (1, 0, 0)} |
|
+0
1
|
|
| 1, 1, 2, 4, 9, 27, 72, 227, 708, 2223, 7676, 25430, 89027, 315152, 1111571, 4083639, 14835745, 54972549, 206172592, 771640657, 2944008745, 11222552195, 43125977024, 167242399629, 648464893456, 2539375564202, 9966074965351, 39263987655425, 155693239075679, 617924738330054, 2466007594800224
(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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A002773 A112706 A110138 this_sequence A003320 A007876 A005095
Adjacent sequences: A148082 A148083 A148084 this_sequence A148086 A148087 A148088
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
|
|
Search completed in 0.002 seconds
|
