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A148554 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, 0), (-1, 1, -1), (-1, 1, 0), (1, 0, 1)}. 1

%I #5 Sep 25 2012 19:34:54

%S 1,1,3,5,23,49,203,461,2191,5417,24179,61093,294551,778881,3591867,

%T 9589629,46607903,128126041,601709315,1661832149,8118460327,

%U 22893192881,108762301515,307387152813,1507018386735,4326952933769,20721610011283,59551484848901,292725740699831,851870785772257,4103481872357339

%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, -1), (-1, -1, 0), (-1, 1, -1), (-1, 1, 0), (1, 0, 1)}.

%H Alois P. Heinz, <a href="/A148554/b148554.txt">Table of n, a(n) for n = 0..600</a>

%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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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 nonn,walk

%O 0,3

%A _Manuel Kauers_, Nov 18 2008

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