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%I #14 Nov 02 2024 04:06:45
%S 16,256,3060,29922,252912,1912914,13254601,85563043,521069404,
%T 3022541224,16826714534,90449485556,471770734372,2397374836954,
%U 11909366979539,57999389713133,277578926336176,1308191004875392,6081976574677816,27936365857925926,126946765412455656
%N Number of nX2 0..3 arrays with row sums unimodal and column sums inverted unimodal
%H R. H. Hardin, <a href="/A223660/b223660.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 31*a(n-1) -437*a(n-2) +3707*a(n-3) -21099*a(n-4) +85029*a(n-5) -249431*a(n-6) +538841*a(n-7) -856504*a(n-8) +988504*a(n-9) -804432*a(n-10) +436752*a(n-11) -141696*a(n-12) +20736*a(n-13).
%F Empirical g.f.: -x*( 16 -240*x +2116*x^2 -12378*x^3 +51142*x^4 -153984*x^5 +342369*x^6 -562536*x^7 +675688*x^8 -578496*x^9 +336528*x^10 -120960*x^11 +20736*x^12) / ( (-1+4*x)^2 *(x-1)^3 *(3*x-1)^4 *(2*x-1)^4 ). - _R. J. Mathar_, May 17 2014
%e Some solutions for n=3:
%e ..3..3....3..2....0..0....0..0....3..1....1..0....1..0....2..0....1..3....3..1
%e ..1..3....2..2....1..3....0..1....0..2....2..1....3..1....0..2....2..3....0..3
%e ..1..1....0..3....3..0....2..0....2..0....0..3....1..2....3..0....1..0....1..0
%Y Column 2 of A223663.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 25 2013