A149020 - OEIS

A149020

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), (-1, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 36, 116, 512, 1904, 8553, 33148, 153051, 618001, 2903351, 12003571, 57034787, 240562562, 1152190595, 4930768743, 23767357634, 102908808435, 498548562369, 2179095365755, 10599171311027, 46692794429830, 227853978702230, 1010419577564144, 4943978183011294, 22047829680652239

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OFFSET

0,3

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A002575 A125792 A223310 * A187980 A057390 A183495

Adjacent sequences: A149017 A149018 A149019 * A149021 A149022 A149023

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved