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A148545 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, 0, 1), (-1, 1, -1), (1, -1, -1), (1, 0, 1)} 0
1, 1, 3, 5, 19, 45, 173, 469, 1915, 5659, 23407, 73243, 310175, 1013731, 4337131, 14639923, 63383137, 219607045, 958081677, 3390264805, 14897264533, 53646021617, 237065064241, 866461879503, 3847927301399, 14243170102087, 63522243469947, 237734050804415, 1064177906517043, 4021244623026059 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148542 A148543 A148544 * A065964 A209778 A148546

Adjacent sequences:  A148542 A148543 A148544 * A148546 A148547 A148548

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)