A150682 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, 0), (-1, 0, -1), (-1, 0, 0), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 26, 114, 424, 1938, 7682, 35932, 147832, 701588, 2958022, 14178258, 60824682, 293639940, 1276150788, 6194167962, 27191889326, 132539041596, 586533927438, 2868470828448, 12777858059712, 62660830011488, 280664690201288, 1379435245569860, 6207447984009842, 30566347449016788, 138098871614655648

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A150679 A150680 A150681 * A303478 A150683 A150684

Adjacent sequences: A150679 A150680 A150681 * A150683 A150684 A150685

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved