A150533 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, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 7, 25, 109, 445, 2041, 8903, 41777, 188835, 898187, 4149843, 19910578, 93363307, 450660409, 2135553110, 10354383193, 49450864210, 240592458544, 1155935532779, 5639339702694, 27222773812905, 133104616214822, 644989013091962, 3159480561138418, 15357981391532350, 75348649206675611

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A005034 A350796 A245157 * A150534 A150535 A076176

Adjacent sequences: A150530 A150531 A150532 * A150534 A150535 A150536

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved