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A150051 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), (0, 0, 1), (0, 1, -1), (0, 1, 0), (1, 0, -1)} 0
1, 2, 6, 18, 61, 220, 831, 3242, 12963, 53065, 221135, 935161, 4004490, 17340560, 75815025, 334224425, 1484309666, 6635773200, 29842139692, 134917595387, 612911928917, 2796639896767, 12811932226760, 58909390903603, 271782665024151, 1257810137283149, 5837979125851679, 27169010031402123 (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, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A150050 A192318 A192483 * A148462 A123639 A228448

Adjacent sequences:  A150048 A150049 A150050 * A150052 A150053 A150054

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 17 17:03 EST 2021. Contains 340247 sequences. (Running on oeis4.)