A150383 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, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 23, 97, 380, 1707, 7232, 33490, 148286, 698883, 3181169, 15165513, 70328453, 337942000, 1588039719, 7674943256, 36419812699, 176783893031, 845159746620, 4116392557523, 19794295312882, 96670463328564, 467018196971056, 2285837694491921, 11084686385891413, 54353664470314740, 264397581795913506

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[-1 + i, j, -1 + k, -1 + n] + aux[i, 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: A150380 A150381 A150382 * A150384 A150385 A047066

Adjacent sequences: A150380 A150381 A150382 * A150384 A150385 A150386

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved