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A148679 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), (0, 0, -1), (1, 0, 1)} 0
1, 1, 3, 7, 21, 73, 229, 777, 2687, 9531, 35431, 128883, 478235, 1784839, 6775523, 26085247, 100114965, 388112537, 1505030269, 5897848369, 23250175625, 91758487101, 364379639057, 1446569914757, 5780001284701, 23157563260401, 93000598894069, 374940517375609, 1511864141405941, 6121906769243097 (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[i, j, 1 + 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: A105795 A244174 A148678 * A148680 A001576 A169587

Adjacent sequences:  A148676 A148677 A148678 * A148680 A148681 A148682

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 23 15:37 EDT 2014. Contains 246000 sequences.