A150651 - OEIS

A150651

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, 0, 0), (0, -1, 1), (0, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 28, 118, 517, 2338, 10779, 50392, 238290, 1136736, 5459706, 26368937, 127941671, 623126153, 3044479214, 14914765582, 73234215657, 360298749816, 1775608806543, 8763377993794, 43306592738488, 214252633433016, 1061035556287348, 5259149506966365, 26087955095040543, 129499032540293441

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150649 A090317 A150650 * A151298 A161944 A150652

Adjacent sequences: A150648 A150649 A150650 * A150652 A150653 A150654

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved