%I #4 Jan 20 2024 14:53:36
%S 1,1,4,13,57,223,1028,4392,20801,93192,448388,2068395,10052266,
%T 47272935,231307163,1102408601,5419992341,26082078971,128680642305,
%U 623701125067,3085177756781,15035715248503,74523449457592,364745828732076,1810638694267339,8891946466493735,44194574931517811,217627063614150518
%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), (1, 1, 0), (1, 1, 0), (1, 0, 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[1 + i, j, 1 + k, 1 + n] + aux[1 + i, 1 + j, k, 1 + n] + aux[1 + i, 1 + j, 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 0,3
%A _Manuel Kauers_, Nov 18 2008
