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A151203 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), (0, 1, -1), (0, 1, 1), (1, 0, 0), (1, 1, 1)}. 0
1, 3, 12, 53, 244, 1150, 5513, 26638, 129726, 634927, 3119000, 15370005, 75910657, 375609808, 1861362004, 9235122359, 45866590554, 227989444738, 1134063002805, 5644442597704, 28107729018221, 140029836266989, 697879124395952, 3479223158959041, 17350384173320732, 86545650442821405 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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}]
CROSSREFS
Sequence in context: A151200 A151201 A151202 * A262442 A026781 A110122
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)