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A150422 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, 0, 1), (1, 0, -1), (1, 0, 1)} 0
1, 2, 7, 24, 95, 381, 1625, 6967, 30701, 136317, 615734, 2798025, 12841240, 59214378, 274997325, 1282425641, 6010338554, 28260119591, 133377022363, 631253981051, 2996520123835, 14257151419520, 67994243210892, 324913086812114, 1555667890089721, 7461052258003051, 35842289376800873, 172433728297469902 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 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: A150419 A150420 A150421 * A137952 A005754 A007162

Adjacent sequences: A150419 A150420 A150421 * A150423 A150424 A150425

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 3 17:51 EST 2022. Contains 358535 sequences. (Running on oeis4.)