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A150418 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), (0, 0, 1), (0, 1, -1), (1, 0, 1)} 0
1, 2, 7, 24, 95, 380, 1597, 6740, 29198, 127139, 561463, 2489928, 11140536, 50028721, 225990649, 1023987562, 4659366057, 21256295772, 97278163016, 446166794259, 2051378747210, 9449478718917, 43614296767443, 201626615220739, 933634601217053, 4329222073486646, 20102125197557820, 93454566326608364 (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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A150415 A150416 A150417 * A150419 A150420 A150421

Adjacent sequences: A150415 A150416 A150417 * A150419 A150420 A150421

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 29 04:47 EST 2023. Contains 359915 sequences. (Running on oeis4.)