# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a149341 Showing 1-1 of 1 %I A149341 #4 Jan 01 2024 18:20:56 %S A149341 1,1,4,12,41,150,568,2173,8481,33756,135463,547375,2233624,9174167, %T A149341 37848374,156914675,653597162,2731737145,11452844102,48166309663, %U A149341 203115207619,858494466299,3636552361349,15436162344558,65641966321937,279610928461517,1192948785566952,5097192013993835 %N A149341 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, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 1)}. %H A149341 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899. %t A149341 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[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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 A149341 nonn,walk %O A149341 0,3 %A A149341 _Manuel Kauers_, Nov 18 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE