A149904 - OEIS

A149904

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

1, 2, 5, 14, 47, 163, 596, 2243, 8806, 34773, 140415, 576389, 2397200, 10036112, 42517170, 181694092, 781065217, 3376828207, 14701304614, 64311598022, 282420505486, 1245793366982, 5518688704385, 24521587743488, 109288995450409, 488683965129030, 2191109757849930, 9846596587883443

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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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A047026 A148338 A149903 * A287888 A115276 A343664

Adjacent sequences: A149901 A149902 A149903 * A149905 A149906 A149907

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved