A149110 - OEIS

%I #5 Nov 05 2025 15:22:13

%S 1,1,4,8,36,94,440,1322,6317,20657,99936,345735,1686163,6072752,

%T 29782403,110551868,544355540,2068820911,10217295294,39572173158,

%U 195880849556,770527923681,3820850450760,15226266849971,75609024577964,304643664710382,1514467671869311,6160177297664718,30651819414993039

%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, -1, 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="https://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[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}]

%K nonn,walk

%O 0,3

%A _Manuel Kauers_, Nov 18 2008