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%I A150262 #4 Dec 29 2023 00:51:06
%S A150262 1,2,6,22,87,365,1570,6882,30754,138898,634681,2925118,13575075,
%T A150262 63414859,297703187,1404068748,6648070472,31583912383,150515794310,
%U A150262 719198068067,3444835940010,16536039844342,79531636649367,383200953238878,1849332507947469,8938198626868800,43259244201766828,209630198366342302
%N A150262 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, 0, 1), (0, 1, 0), (1, 0, -1), (1, 0, 1)}.
%H A150262 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 A150262 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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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 A150262 nonn,walk
%O A150262 0,2
%A A150262 _Manuel Kauers_, Nov 18 2008

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