login
A151045
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, -1, 0), (0, 1, 0), (0, 1, 1), (1, 0, 1)}.
0
1, 3, 9, 35, 141, 551, 2329, 9995, 42101, 184463, 815153, 3557395, 15904077, 71496471, 318526473, 1442648027, 6559367461, 29621184159, 135382970721, 620554541987, 2829281958269, 13018531716903, 60037006978617, 275683433405803, 1275128230497365, 5908434075541167, 27280995507241105, 126707183319906099
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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A149019 A102865 A046697 * A369389 A225041 A335642
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved