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A237570 Number of (n+1)X(2+1) 0..3 arrays with the upper median minus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one.

%I A237570 #6 Jul 23 2025 10:18:53
%S A237570 1876,24332,315664,4146324,54395184,712810024,9341685548,122455823868,
%T A237570 1605139419940,21039580744172,275778485963796,3614821845795620,
%U A237570 47382014286972468,621068632282931188,8140767996582698140
%N A237570 Number of (n+1)X(2+1) 0..3 arrays with the upper median minus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one.
%C A237570 Column 2 of A237574
%H A237570 R. H. Hardin, <a href="/A237570/b237570.txt">Table of n, a(n) for n = 1..210</a>
%F A237570 Empirical: a(n) = 22*a(n-2) +717*a(n-3) +9851*a(n-4) +58039*a(n-5) +282363*a(n-6) +932626*a(n-7) +763157*a(n-8) -5054633*a(n-9) -31588581*a(n-10) -115776674*a(n-11) -160827826*a(n-12) +333525933*a(n-13) +1758583042*a(n-14) +2964658024*a(n-15) +49163147*a(n-16) -10533038460*a(n-17) -24197541615*a(n-18) -20964618288*a(n-19) +43163041975*a(n-20) +142771631658*a(n-21) +71165049213*a(n-22) -205125362959*a(n-23) -286625063582*a(n-24) +3665735376*a(n-25) +250982853215*a(n-26) +153419401277*a(n-27) +29910572638*a(n-28) +69334272134*a(n-29) +26030554320*a(n-30) -157877752948*a(n-31) -279343069536*a(n-32) -104462683872*a(n-33) +65989529824*a(n-34) +87578561472*a(n-35) +21371116928*a(n-36) -36675133952*a(n-37) -23711340544*a(n-38) -4557326336*a(n-39) -796352512*a(n-40) -238338048*a(n-41) +625999872*a(n-42) -578551808*a(n-43) -315621376*a(n-44) -50331648*a(n-45)
%e A237570 Some solutions for n=2
%e A237570 ..2..1..2....2..1..3....2..1..1....0..2..2....3..0..1....1..1..0....0..1..0
%e A237570 ..2..3..0....3..0..3....2..3..2....1..3..2....3..1..0....3..0..3....1..2..0
%e A237570 ..3..1..1....1..3..0....1..0..0....2..2..3....2..1..2....1..0..2....1..3..0
%K A237570 nonn
%O A237570 1,1
%A A237570 _R. H. Hardin_, Feb 09 2014