A150645 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), (0, 0, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 2, 7, 27, 119, 532, 2493, 11751, 56526, 272852, 1330410, 6502103, 31952536, 157280769, 776671738, 3839959233, 19022898390, 94323668554, 468299922839, 2326622294614, 11569292283782, 57559421076093, 286544762335029, 1427071552401897, 7110370388498281, 35438671133831670, 176687791134419279

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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: A007166 A036783 A368762 * A060017 A211475 A213226

Adjacent sequences: A150642 A150643 A150644 * A150646 A150647 A150648

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved