A068724 Number of solenoidal flows (flow in = flow out) in a 5 X 5 square array with integer velocities -n .. n.

1, 569397, 1305759171, 251611610655, 13336307324915, 322309309862183

Offset

0,2

Links

Table of n, a(n) for n=0..5.

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.
5 X 5 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0 . 0 . 0
.0. -1. -1. -1. -1 . 0
.. 1 . 0 . 0 . 0. -1
.0 . 0. -1. -1 . 0 . 0
.. 1 . 1 . 0. -1. -1
.0 . 0 . 0 . 0 . 0 . 0
.. 1 . 1 . 0. -1. -1
.0 . 0 . 1 . 1 . 0 . 0
.. 1 . 0 . 0 . 0. -1
.0 . 1 . 1 . 1 . 1 . 0
.. 0 . 0 . 0 . 0 . 0
n=2:
.. 0 . 0 . 0 . 0 . 0
.0. -2. -1. -1. -1 . 0
.. 2. -1 . 0 . 0. -1
.0 . 0. -2. -2. -1 . 0
.. 2 . 1 . 0. -1. -2
.0 . 0. -1. -1 . 0 . 0
.. 2 . 2 . 0. -2. -2
.0 . 0 . 2 . 2 . 0 . 0
.. 2 . 0 . 0 . 0. -2
.0 . 2 . 2 . 2 . 2 . 0
.. 0 . 0 . 0 . 0 . 0

Crossrefs

Cf. 2 X 2=1, 3, 5, 7..., 3 X 3 A068722, 4 X 4 A068723, 6x6 A068725, by velocity limit 1..13 A068726-A068738.

Sequence in context: A237935 A237693 A156412 * A233651 A288085 A121169

Adjacent sequences: A068721 A068722 A068723 * A068725 A068726 A068727

Keyword

nonn

Author

R. H. Hardin, Feb 26 2002

Status

approved