A149494 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, 1), (-1, 1, 1), (1, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 14, 63, 255, 1208, 5300, 25641, 117338, 573977, 2692760, 13258820, 63201086, 312496952, 1505774619, 7466107255, 36252353187, 180100006382, 879419719458, 4375006206173, 21453621299034, 106838674543666, 525615953548604, 2619579742968437, 12920694277538078, 64432646543341008, 318456275901964557

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, 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, -1 + k, -1 + n] + aux[1 + i, 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: A009339 A050912 A250399 * A322206 A149495 A137956

Adjacent sequences: A149491 A149492 A149493 * A149495 A149496 A149497

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved