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A150274 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, 1, 1), (1, 0, 1), (1, 1, -1)}. 0
1, 2, 6, 22, 94, 370, 1682, 7138, 32882, 146614, 682866, 3120066, 14730854, 68233982, 325456138, 1524123022, 7313477578, 34576073774, 166582262834, 793435987550, 3836131459466, 18373065673338, 89115810052902, 428673021509750, 2084820152654090, 10065304671767582, 49058336646592546, 237596508078093598 (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, -1 + k, -1 + n] + aux[i, -1 + 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}]
CROSSREFS
Sequence in context: A317652 A374544 A374545 * A109317 A109153 A030453
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 18 01:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)