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A149899 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, 0, 0), (0, 1, 0), (0, 1, 1), (1, -1, -1)}. 0

%I #4 Jan 16 2024 09:54:18

%S 1,2,5,14,47,159,565,2063,7865,30157,118017,469064,1892519,7681288,

%T 31525714,130593424,544754098,2284273316,9645909083,40963272701,

%U 174700576880,748259285162,3219949393396,13907429430622,60257237322969,261964987031169,1142598100016005,4996769804097317

%N 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, 0, 0), (0, 1, 0), (0, 1, 1), (1, -1, -1)}.

%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.

%t 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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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}]

%K nonn,walk

%O 0,2

%A _Manuel Kauers_, Nov 18 2008

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Last modified March 28 13:35 EDT 2024. Contains 371254 sequences. (Running on oeis4.)