cp's OEIS Frontend

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

%I A068724 #13 Mar 06 2024 21:48:14
%S A068724 1,569397,1305759171,251611610655,13336307324915,322309309862183,
%T A068724 4598900066440609,44976296745414509,331136639667811845,
%U A068724 1954290045098180729,9661874271897648847,41320247284448146619,156588834507399529975
%N A068724 Number of solenoidal flows (flow in = flow out) in a 5 X 5 square array with integer velocities -n .. n.
%e A068724 Sample flows (. represents a space):
%e A068724 Numbers in long rows are on cell walls showing velocity rightward.
%e A068724 Numbers in long columns are on cell floors showing velocity downwards.
%e A068724 5 X 5 cell centers are at the intersection of long rows and long columns.
%e A068724 n=1:
%e A068724 .. 0 . 0 . 0 . 0 . 0
%e A068724 .0. -1. -1. -1. -1 . 0
%e A068724 .. 1 . 0 . 0 . 0. -1
%e A068724 .0 . 0. -1. -1 . 0 . 0
%e A068724 .. 1 . 1 . 0. -1. -1
%e A068724 .0 . 0 . 0 . 0 . 0 . 0
%e A068724 .. 1 . 1 . 0. -1. -1
%e A068724 .0 . 0 . 1 . 1 . 0 . 0
%e A068724 .. 1 . 0 . 0 . 0. -1
%e A068724 .0 . 1 . 1 . 1 . 1 . 0
%e A068724 .. 0 . 0 . 0 . 0 . 0
%e A068724 n=2:
%e A068724 .. 0 . 0 . 0 . 0 . 0
%e A068724 .0. -2. -1. -1. -1 . 0
%e A068724 .. 2. -1 . 0 . 0. -1
%e A068724 .0 . 0. -2. -2. -1 . 0
%e A068724 .. 2 . 1 . 0. -1. -2
%e A068724 .0 . 0. -1. -1 . 0 . 0
%e A068724 .. 2 . 2 . 0. -2. -2
%e A068724 .0 . 0 . 2 . 2 . 0 . 0
%e A068724 .. 2 . 0 . 0 . 0. -2
%e A068724 .0 . 2 . 2 . 2 . 2 . 0
%e A068724 .. 0 . 0 . 0 . 0 . 0
%Y A068724 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.
%K A068724 nonn
%O A068724 0,2
%A A068724 _R. H. Hardin_, Feb 26 2002
%E A068724 a(6)-a(12) from _Sean A. Irvine_, Mar 06 2024