# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a149374 Showing 1-1 of 1 %I A149374 #4 Jan 06 2024 02:37:34 %S A149374 1,1,4,12,47,162,711,2793,12113,49196,221666,942290,4229610,18235322, %T A149374 83386846,367729931,1678926008,7460343556,34432541595,155038893329, %U A149374 715065882121,3234817528840,15025104684796,68555045599390,318330259560687,1457036761790380,6799065794238751,31305388241800917 %N A149374 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, 1), (-1, 1, 1), (0, 0, -1), (0, 1, -1), (1, 0, 1)}. %H A149374 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899. %t A149374 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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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 A149374 nonn,walk %O A149374 0,3 %A A149374 _Manuel Kauers_, Nov 18 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE