A150185 - OEIS

A150185

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

1, 2, 6, 20, 80, 304, 1198, 4880, 20196, 84392, 356572, 1520772, 6530176, 28222746, 122757040, 536408010, 2353654246, 10369862958, 45853776044, 203408616728, 904980106270, 4037154470484, 18054334964388, 80924856101506, 363506260495212, 1636056488860916, 7376962377565698, 33319803053180324

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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, 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, 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: A300514 A150183 A150184 * A354737 A357502 A187009

Adjacent sequences: A150182 A150183 A150184 * A150186 A150187 A150188

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved