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A149762 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), (-1, 0, 1), (0, -1, 0), (0, 1, -1), (1, 1, 1)}. 0
1, 1, 5, 19, 71, 295, 1235, 5295, 23067, 100741, 446333, 1990923, 8921577, 40238639, 182135331, 827660543, 3774668091, 17261298041, 79153761795, 363820343771, 1675729140379, 7733588756085, 35753310200333, 165557637678259, 767768829923499, 3565349366295773, 16577672292312341, 77171680837508353 (list; graph; refs; listen; history; text; internal format)
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, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + 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: A149759 A149760 A149761 * A299107 A086386 A343799
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified February 25 13:12 EST 2024. Contains 370330 sequences. (Running on oeis4.)