|
|
A151201
|
|
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, 1), (1, 0, 1), (1, 1, 0)}
|
|
0
|
|
|
1, 3, 12, 53, 243, 1141, 5459, 26346, 128168, 626971, 3078529, 15165364, 74884171, 370462126, 1835612406, 9106519567, 45224396045, 224785228719, 1118079087396, 5564712384177, 27710087105226, 138046537190474, 687986650617224, 3429877906752834, 17104214087353510, 85317456980257087
(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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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
|
|
|
|