A150862 - OEIS

A150862

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

1, 2, 8, 32, 143, 646, 3013, 14216, 67939, 327200, 1585980, 7725527, 37777737, 185320840, 911426406, 4492064943, 22178844495, 109668362611, 542968554654, 2691156370891, 13350845387786, 66287180191579, 329348650810692, 1637379870230403, 8144751559357207, 40533435385906476, 201805270245783128

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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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + 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: A308368 A072243 A150861 * A150863 A084137 A129400

Adjacent sequences: A150859 A150860 A150861 * A150863 A150864 A150865

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved