|
| |
|
|
A150269
|
|
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), (0, 1, -1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.
|
|
0
|
|
|
|
1, 2, 6, 22, 90, 375, 1632, 7228, 32542, 148889, 687558, 3203532, 15035292, 70959865, 336619928, 1603694686, 7667719866, 36781517568, 176929341895, 853188421537, 4123375152801, 19966905610364, 96858581103837, 470608107771531, 2289852607790047, 11156510971249147, 54421608462422660, 265761980956092284
(list;
graph;
refs;
listen;
history;
text;
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, k, -1 + n] + aux[i, -1 + j, 1 + 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
|
|
|
|
KEYWORD
|
nonn,walk
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
