cp's OEIS Frontend

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

%I A068725 #10 Mar 07 2024 19:50:05
%S A068725 1,758541101,134771061592765,500885416261650533,247753867499441888279,
%T A068725 35922392489639958547367,2286173927365217148894607,
%U A068725 80633423581611695455020595
%N A068725 Number of solenoidal flows (flow in = flow out) in a 6x6 square array with integer velocities -n .. n.
%e A068725 Sample flows (. represents a space):
%e A068725 Numbers in long rows are on cell walls showing velocity rightward.
%e A068725 Numbers in long columns are on cell floors showing velocity downwards.
%e A068725 6x6 cell centers are at the intersection of long rows and long columns.
%e A068725 n=1:
%e A068725 .. 0 . 0 . 0 . 0 . 0 . 0
%e A068725 .0. -1. -1. -1. -1. -1 . 0
%e A068725 .. 1 . 0 . 0 . 0 . 0. -1
%e A068725 .0 . 0. -1. -1. -1 . 0 . 0
%e A068725 .. 1 . 1 . 0 . 0. -1. -1
%e A068725 .0 . 0 . 0. -1 . 0 . 0 . 0
%e A068725 .. 1 . 1 . 1. -1. -1. -1
%e A068725 .0 . 0 . 0 . 1 . 0 . 0 . 0
%e A068725 .. 1 . 1 . 0 . 0. -1. -1
%e A068725 .0 . 0 . 1 . 1 . 1 . 0 . 0
%e A068725 .. 1 . 0 . 0 . 0 . 0. -1
%e A068725 .0 . 1 . 1 . 1 . 1 . 1 . 0
%e A068725 .. 0 . 0 . 0 . 0 . 0 . 0
%e A068725 n=2:
%e A068725 .. 0 . 0 . 0 . 0 . 0 . 0
%e A068725 .0. -2. -1. -1 . 0. -1 . 0
%e A068725 .. 2. -1 . 0. -1 . 1. -1
%e A068725 .0 . 0. -2. -2. -2. -1 . 0
%e A068725 .. 2 . 1 . 0. -1 . 0. -2
%e A068725 .0 . 0. -1. -2. -2 . 0 . 0
%e A068725 .. 2 . 2 . 1. -1. -2. -2
%e A068725 .0 . 0 . 0 . 1 . 0 . 0 . 0
%e A068725 .. 2 . 2 . 0 . 0. -2. -2
%e A068725 .0 . 0 . 2 . 2 . 2 . 0 . 0
%e A068725 .. 2 . 0 . 0 . 0 . 0. -2
%e A068725 .0 . 2 . 2 . 2 . 2 . 2 . 0
%e A068725 .. 0 . 0 . 0 . 0 . 0 . 0
%Y A068725 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.
%K A068725 nonn,more
%O A068725 0,2
%A A068725 _R. H. Hardin_, Feb 26 2002
%E A068725 a(4)-a(7) from _Sean A. Irvine_, Mar 07 2024