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A149260
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), (1, 0, -1), (1, 1, 1)}.
0
1, 1, 4, 11, 40, 122, 468, 1567, 6112, 21162, 83196, 296598, 1170760, 4259252, 16858192, 62189887, 246726504, 919595326, 3654991076, 13734831550, 54659800248, 206768895132, 823609387928, 3132526493386, 12486623852344, 47705231049608, 190272793552880, 729685146355196, 2911758222803120
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, 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
Sequence in context: A366695 A149259 A050911 * A149261 A149262 A149263
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved