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A149840 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, -1), (0, 1, 0), (1, 0, 0)} 0
1, 2, 4, 12, 36, 105, 359, 1234, 4179, 15184, 55991, 204578, 771394, 2964054, 11327531, 43884270, 172977384, 680790080, 2693644347, 10800095655, 43381674853, 174545003823, 708672027933, 2888280123869, 11778061217176, 48301653756423, 198967324198300, 820165234102410, 3391901879073496 (list; graph; refs; listen; history; text; internal format)
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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A149838 A192236 A149839 * A224540 A025579 A214936

Adjacent sequences:  A149837 A149838 A149839 * A149841 A149842 A149843

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 28 08:33 EDT 2020. Contains 337394 sequences. (Running on oeis4.)