A150663 - OEIS

%I #4 Jan 20 2024 18:12:39

%S 1,2,7,29,127,578,2694,12777,61311,296687,1444610,7067651,34706412,

%T 170926789,843757686,4172911941,20669327222,102509183526,508927584984,

%U 2528902166589,12575676943431,62575687839661,311540887849208,1551767773859324,7732381378091565,38543552002276177,192186472317221319

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

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