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A148849
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, 0, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.
1
1, 1, 3, 8, 28, 91, 330, 1158, 4301, 15704, 59202, 221160, 842264, 3192043, 12246092, 46861680, 180776672, 696518376, 2698468580, 10449533172, 40622230498, 157911491626, 615583136488, 2400206401102, 9378223581365, 36655425305228, 143499450616324, 561998883034538, 2203752597514260
OFFSET
0,3
LINKS
A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008.
MAPLE
Steps:= [[-1, 0, 1], [1, -1, 1], [1, 0, 1], [1, 1, -1]]:
f:= proc(n, p) option remember;
if n <= min(p) then return 4^n fi;
add(procname(n-1, t), t=remove(has, map(`+`, Steps, p), -1));
end proc:
map(f, [$0..40], [0, 0, 0]); # Robert Israel, May 01 2018
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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A163062 A148847 A148848 * A148850 A148851 A148852
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved