cp's OEIS Frontend

A068723 Number of solenoidal flows (flow in = flow out) in a 4 X 4 square array with integer velocities -n .. n.

%I A068723 #16 Mar 06 2024 04:26:55
%S A068723 1,2053,160403,3096791,28905785,173429597,773568107,2789847759,
%T A068723 8576204625,23279942261,57201104003,129540052071,274074872265,
%U A068723 547436323149,1040787422427,1895867410719,3326525754145,5647051042021,9308792104563,14946774417783,23438233878745,35975222324029,54153684727627,80081666851567,116509584233329
%N A068723 Number of solenoidal flows (flow in = flow out) in a 4 X 4 square array with integer velocities -n .. n.
%H A068723 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a068/A068723.java">Java program</a> (github)
%F A068723 Empirical G.f.: (x+1) * (x^8 + 2042*x^7 + 137876*x^6 + 1447150*x^5 + 3462710*x^4 + 1447150*x^3 + 137876*x^2 + 2042*x + 1) / (x-1)^10. [_Colin Barker_, Jul 31 2012]
%e A068723 Sample flows (. represents a space):
%e A068723 Numbers in long rows are on cell walls showing velocity rightward.
%e A068723 Numbers in long columns are on cell floors showing velocity downwards.
%e A068723 4 X 4 cell centers are at the intersection of long rows and long columns.
%e A068723 n=1:
%e A068723 .. 0 . 0 . 0 . 0
%e A068723 .0. -1. -1. -1 . 0
%e A068723 .. 1 . 0 . 0. -1
%e A068723 .0 . 0. -1 . 0 . 0
%e A068723 .. 1 . 1. -1. -1
%e A068723 .0 . 0 . 1 . 0 . 0
%e A068723 .. 1 . 0 . 0. -1
%e A068723 .0 . 1 . 1 . 1 . 0
%e A068723 .. 0 . 0 . 0 . 0
%e A068723 n=2:
%e A068723 .. 0 . 0 . 0 . 0
%e A068723 .0. -2. -1. -2 . 0
%e A068723 .. 2. -1 . 1. -2
%e A068723 .0 . 0. -2 . 0 . 0
%e A068723 .. 2 . 1. -1. -2
%e A068723 .0 . 0 . 1 . 0 . 0
%e A068723 .. 2 . 0 . 0. -2
%e A068723 .0 . 2 . 2 . 2 . 0
%e A068723 .. 0 . 0 . 0 . 0
%Y A068723 Cf. A005408 (2 X 2), A068722 (3 X 3), A068724 (5 X 5), A068725 (6 X 6).
%Y A068723 By velocity limit 1..13 A068726-A068738.
%K A068723 nonn
%O A068723 0,2
%A A068723 _R. H. Hardin_, Feb 26 2002
%E A068723 a(14)-a(24) from _Sean A. Irvine_, Mar 06 2024