A148859 - OEIS

A148859

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

1, 1, 3, 8, 28, 96, 349, 1294, 4900, 19175, 75820, 304450, 1237879, 5080610, 21057345, 87889165, 369769072, 1565029070, 6660413594, 28504725054, 122534388266, 529047867652, 2293336147592, 9977416694579, 43555434463046, 190726313779884, 837672138930133, 3689004196873598, 16287162984427420

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OFFSET

0,3

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, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A273162 A148857 A148858 * A148860 A148861 A148862

Adjacent sequences: A148856 A148857 A148858 * A148860 A148861 A148862

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved