|
Search: id:A148575
|
|
|
| A148575 |
|
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), (-1, 0, 1), (1, 0, 0), (1, 1, -1)} |
|
+0
1
|
|
| 1, 1, 3, 6, 20, 50, 181, 513, 1981, 6087, 24450, 79265, 326192, 1098561, 4604660, 15968636, 67934917, 241144724, 1037831560, 3753744245, 16303956286, 59889623003, 262114436704, 975484574708, 4296973313554, 16171297126704, 71624751796375, 272169868078628, 1211149718585558, 4641314003656235
(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[-1 + i, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
|
|
CROSSREFS
|
Sequence in context: A148574 A005558 A138350 this_sequence A148576 A148577 A148578
Adjacent sequences: A148572 A148573 A148574 this_sequence A148576 A148577 A148578
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
|
|
Search completed in 0.002 seconds
|
