# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a149830 Showing 1-1 of 1 %I A149830 #4 Jan 16 2024 10:04:29 %S A149830 1,2,4,10,28,85,282,961,3348,12090,44786,168404,643901,2505895, %T A149830 9858281,39170311,157508249,638763140,2608585552,10740130403, %U A149830 44524221312,185571516895,777920112939,3279160755069,13883250806461,59032846349700,252125642478286,1080805369925001,4648940165418700 %N A149830 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), (1, -1, 0), (1, 0, 0)}. %H A149830 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899. %t A149830 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, k, -1 + n] + aux[-1 + i, 1 + j, 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 A149830 nonn,walk %O A149830 0,2 %A A149830 _Manuel Kauers_, Nov 18 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE