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A150101 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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, -1)} 0
1, 2, 6, 19, 68, 253, 982, 3904, 15904, 65870, 276702, 1176029, 5049443, 21864431, 95369300, 418700058, 1848734071, 8204001286, 36570660638, 163685587764, 735324507172, 3314279623363, 14983732949119, 67929967517380, 308753250967957, 1406646255864308, 6422545729056850, 29383868785665040 (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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A007721 A150099 A150100 * A150102 A150103 A150104

Adjacent sequences:  A150098 A150099 A150100 * A150102 A150103 A150104

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 19 22:04 EST 2020. Contains 332060 sequences. (Running on oeis4.)