A149539 - OEIS

A149539

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

1, 1, 5, 13, 51, 179, 707, 2631, 10657, 41565, 169871, 679473, 2811927, 11431875, 47657045, 196290401, 823740077, 3422948805, 14440656985, 60463251011, 256164359217, 1078817656205, 4587846008299, 19416320438649, 82826258472915, 351972270623525, 1505603231596009, 6420270536168731

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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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + 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: A238508 A151274 A149538 * A007231 A158345 A372370

Adjacent sequences: A149536 A149537 A149538 * A149540 A149541 A149542

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved