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A148320
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, 0, 0), (0, -1, 0), (0, 0, 1), (1, 1, -1)}.
0
1, 1, 2, 5, 14, 40, 120, 375, 1212, 3976, 13262, 44928, 154484, 536046, 1876504, 6623171, 23568612, 84362580, 303647530, 1098556826, 3994948648, 14586549832, 53462105550, 196642390104, 725847534220, 2687112563572, 9975411747458, 37128042125870, 138546640163748, 518147055726962, 1941898830982032
OFFSET
0,3
LINKS
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
MATHEMATICA
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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
CROSSREFS
Sequence in context: A200438 A363933 A103140 * A374541 A301871 A076866
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved