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A149585
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, 0), (-1, -1, 1), (-1, 0, 1), (0, 0, -1), (1, 1, 1)}
1
1, 1, 5, 15, 55, 203, 791, 3041, 12057, 48249, 194705, 790373, 3237213, 13323957, 55078721, 228709819, 953594747, 3988265595, 16730145283, 70382381531, 296830291631, 1254604475451, 5314036803363, 22552374316543, 95878895567139, 408287637231539, 1741343710323743, 7437497858831271
OFFSET
0,3
LINKS
Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2009.
MAPLE
Steps:= [[-1, -1, 0], [-1, -1, 1], [-1, 0, 1], [0, 0, -1], [1, 1, 1] ]:
f:= proc(n, p) option remember;
if n <= min(p) then return 5^n fi;
add(procname(n-1, t), t=remove(has, map(`+`, Steps, p), -1));
end proc:
map(f, [$0..30], [0, 0, 0]); # Robert Israel, Feb 27 2022
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[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A123011 A006358 A054108 * A114947 A316104 A149586
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved