A148932 - OEIS

%I #4 Mar 29 2024 19:50:27

%S 1,1,3,9,28,97,349,1302,4948,19260,76305,306502,1244827,5110421,

%T 21175303,88391007,371584013,1571765178,6684742369,28573868325,

%U 122690873139,528944280447,2289098069619,9940723089700,43304254195744,189206292581281,828943812897922,3640845471311392,16029356622087075

%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, 1), (0, 1, 1), (1, 0, -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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + 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 0,3

%A _Manuel Kauers_, Nov 18 2008