A068725 Number of solenoidal flows (flow in = flow out) in a 6x6 square array with integer velocities -n .. n.

1, 758541101, 134771061592765, 500885416261650533, 247753867499441888279, 35922392489639958547367, 2286173927365217148894607, 80633423581611695455020595

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Example

Sample flows (. represents a space):
Numbers in long rows are on cell walls showing velocity rightward.
Numbers in long columns are on cell floors showing velocity downwards.
6x6 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0 . 0 . 0 . 0
.0. -1. -1. -1. -1. -1 . 0
.. 1 . 0 . 0 . 0 . 0. -1
.0 . 0. -1. -1. -1 . 0 . 0
.. 1 . 1 . 0 . 0. -1. -1
.0 . 0 . 0. -1 . 0 . 0 . 0
.. 1 . 1 . 1. -1. -1. -1
.0 . 0 . 0 . 1 . 0 . 0 . 0
.. 1 . 1 . 0 . 0. -1. -1
.0 . 0 . 1 . 1 . 1 . 0 . 0
.. 1 . 0 . 0 . 0 . 0. -1
.0 . 1 . 1 . 1 . 1 . 1 . 0
.. 0 . 0 . 0 . 0 . 0 . 0
n=2:
.. 0 . 0 . 0 . 0 . 0 . 0
.0. -2. -1. -1 . 0. -1 . 0
.. 2. -1 . 0. -1 . 1. -1
.0 . 0. -2. -2. -2. -1 . 0
.. 2 . 1 . 0. -1 . 0. -2
.0 . 0. -1. -2. -2 . 0 . 0
.. 2 . 2 . 1. -1. -2. -2
.0 . 0 . 0 . 1 . 0 . 0 . 0
.. 2 . 2 . 0 . 0. -2. -2
.0 . 0 . 2 . 2 . 2 . 0 . 0
.. 2 . 0 . 0 . 0 . 0. -2
.0 . 2 . 2 . 2 . 2 . 2 . 0
.. 0 . 0 . 0 . 0 . 0 . 0

Crossrefs

2 X 2 gives 1, 3, 5, 7..., 3 X 3 gives A068722, 4 X 4 gives A068723, 5 X 5 gives A068724, by velocity limit 1..13 A068726-A068738.

Sequence in context: A035518 A104952 A015370 * A104932 A306569 A118876

Adjacent sequences: A068722 A068723 A068724 * A068726 A068727 A068728

Keyword

nonn,more

Author

R. H. Hardin, Feb 26 2002

Extensions

a(4)-a(7) from Sean A. Irvine, Mar 07 2024

Status

approved