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A150655 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, 0), (-1, 1, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}. 0
1, 2, 7, 28, 120, 526, 2381, 10922, 50757, 238129, 1125448, 5350048, 25556511, 122562645, 589753134, 2845909120, 13766991676, 66739791983, 324149453400, 1576978364648, 7683288284434, 37483722315418, 183086192515193, 895234712523878, 4381718084447971, 21465519743894719, 105243595782959115 (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, 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: A130655 A150653 A150654 * A005436 A150656 A150657
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 19 16:52 EDT 2024. Contains 371794 sequences. (Running on oeis4.)