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A150031 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), (-1, 1, 0), (1, 0, 0), (1, 0, 1)} 0
1, 2, 6, 16, 62, 209, 826, 2884, 12327, 46607, 197833, 754220, 3343667, 13318517, 58434940, 233005648, 1052872124, 4322695836, 19330561228, 79239584849, 362301103486, 1517546326245, 6870981921627, 28703048456221, 132297147943855, 562147041928433, 2567582959610258, 10875375405053705 (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, j, -1 + k, -1 + n] + aux[-1 + i, j, 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, 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: A197102 A093113 A150030 * A121753 A173994 A150032

Adjacent sequences:  A150028 A150029 A150030 * A150032 A150033 A150034

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 27 06:26 EDT 2021. Contains 348271 sequences. (Running on oeis4.)