A150186 - OEIS

A150186

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

1, 2, 6, 21, 74, 283, 1118, 4458, 18351, 76591, 321854, 1374658, 5918280, 25602941, 111845103, 491194938, 2164765075, 9602560058, 42758955587, 190902880964, 856275025748, 3851882921655, 17363060613832, 78540508309270, 356080409031020, 1617037125714653, 7363291071152261, 33590693707602351

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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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A294769 A116738 A360151 * A150187 A116818 A294770

Adjacent sequences: A150183 A150184 A150185 * A150187 A150188 A150189

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved