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A148330 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, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, -1)} 0
1, 1, 2, 5, 14, 42, 134, 450, 1561, 5584, 20384, 76110, 288678, 1111867, 4332969, 17081566, 68003151, 273141366, 1105621792, 4507122693, 18493763341, 76333387299, 316764690900, 1320956750386, 5533915084459, 23281928699430, 98335287674627, 416846016334321, 1773046351548880, 7565766894106024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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[1 + 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: A346660 A129086 A035052 * A149876 A165146 A148331

Adjacent sequences:  A148327 A148328 A148329 * A148331 A148332 A148333

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 24 12:01 EDT 2022. Contains 354033 sequences. (Running on oeis4.)