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