A150654 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, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 28, 120, 525, 2387, 10919, 50974, 238801, 1131589, 5377188, 25727692, 123387617, 594364897, 2868769619, 13888104107, 67345509405, 327276382110, 1592650418185, 7763092692040, 37883707939065, 185107350039596, 905358387895978, 4432641740587092, 21720393028457062, 106522062196071109

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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: A150652 A130655 A150653 * A150655 A005436 A150656

Adjacent sequences: A150651 A150652 A150653 * A150655 A150656 A150657

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved