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, 4598900066440609, 44976296745414509, 331136639667811845, 1954290045098180729, 9661874271897648847, 41320247284448146619, 156588834507399529975

Offset: 0

Author

R. H. Hardin, Feb 26 2002

Keywords

• nonn

Examples

			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.

Extensions

a(6)-a(12) from Sean A. Irvine, Mar 06 2024