A149044 - OEIS

A149044

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

1, 1, 3, 10, 37, 141, 581, 2410, 10360, 44924, 198919, 886599, 4001741, 18167569, 83200913, 382777451, 1771864969, 8233910451, 38441078019, 180044247192, 846284724044, 3988788929314, 18854489257593, 89329187127811, 424223002744866, 2018647242982408, 9624634711205182, 45967961675464498

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OFFSET

0,3

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A151049 A195350 A289810 * A105284 A211975 A357399

Adjacent sequences: A149041 A149042 A149043 * A149045 A149046 A149047

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved