A149827 - OEIS

A149827

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

1, 2, 4, 10, 28, 85, 282, 947, 3248, 11612, 42236, 156527, 590013, 2243611, 8656634, 33776331, 132719867, 526382525, 2102410851, 8450274733, 34194734301, 139059227367, 568371318740, 2334597118201, 9627877133915, 39868088607697, 165703572469009, 690995265813717, 2891083031904521

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, 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: A135336 A149825 A149826 * A149828 A149829 A149830

Adjacent sequences: A149824 A149825 A149826 * A149828 A149829 A149830

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved