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A149884 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, 0), (1, 1, 0)} 0
1, 2, 5, 14, 44, 151, 530, 1956, 7333, 28175, 110374, 438557, 1766533, 7185329, 29576438, 122613969, 512239312, 2156329253, 9129063620, 38862836164, 166293448143, 715081979684, 3086928355364, 13378595285185, 58208937327489, 254060121142994, 1112288142183214, 4884520416003977 (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, k, -1 + n] + aux[-1 + i, j, 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: A268419 A149883 A307786 * A149885 A149886 A207081

Adjacent sequences:  A149881 A149882 A149883 * A149885 A149886 A149887

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 7 12:30 EDT 2022. Contains 355986 sequences. (Running on oeis4.)