A150203 - OEIS

A150203

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

1, 2, 6, 21, 80, 322, 1347, 5796, 25477, 113874, 515818, 2362069, 10914502, 50815843, 238113099, 1121913889, 5311353117, 25249666932, 120473327642, 576668900224, 2768258625991, 13322888865844, 64266963824287, 310653575562268, 1504452962143164, 7298269464489332, 35459668011919995, 172530211194057549

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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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A352703 A352704 A257561 * A106228 A150204 A129442

Adjacent sequences: A150200 A150201 A150202 * A150204 A150205 A150206

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved