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A151243
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, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 1)}
0
1, 4, 16, 68, 302, 1368, 6286, 29252, 137362, 649364, 3087370, 14748464, 70725462, 340273352, 1641776542, 7940754972, 38488807306, 186906855308, 909163023138, 4428993280472, 21604758800206, 105516100105312, 515897991437334, 2524889027988452, 12368504179077730, 60639542760057540, 297529289813602874
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[i, 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: A089979 A179191 A128730 * A006319 A202020 A059606
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved