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A201216 T(n,k)=Number of nXk 0..3 arrays with every row and column running average nondecreasing rightwards and downwards.

%I A201216 #7 Jul 22 2025 16:09:48
%S A201216 4,10,10,23,50,23,51,216,216,51,110,867,1684,867,110,233,3318,11932,
%T A201216 11932,3318,233,488,12314,79739,146946,79739,12314,488,1013,44858,
%U A201216 512681,1692945,1692945,512681,44858,1013,2088,161257,3216277,18624423,33635880
%N A201216 T(n,k)=Number of nXk 0..3 arrays with every row and column running average nondecreasing rightwards and downwards.
%C A201216 Table starts
%C A201216 ....4......10........23...........51............110.............233
%C A201216 ...10......50.......216..........867...........3318...........12314
%C A201216 ...23.....216......1684........11932..........79739..........512681
%C A201216 ...51.....867.....11932.......146946........1692945........18624423
%C A201216 ..110....3318.....79739......1692945.......33635880.......638359663
%C A201216 ..233...12314....512681.....18624423......638359663.....21062625664
%C A201216 ..488...44858...3216277....198262359....11689716107....671706552402
%C A201216 .1013..161257..19817136...2055746385...207621805136..20756983300265
%C A201216 .2088..574237.120478844..20869314255..3594844603992.624562355419649
%C A201216 .4278.2029778.724707450.208139081237.60914727372933
%H A201216 R. H. Hardin, <a href="/A201216/b201216.txt">Table of n, a(n) for n = 1..111</a>
%e A201216 Some solutions for n=4 k=4
%e A201216 ..0..0..2..1....0..0..1..1....0..0..0..0....0..0..0..1....0..0..0..1
%e A201216 ..0..0..3..1....0..1..2..2....0..0..2..3....0..0..1..1....0..0..1..1
%e A201216 ..3..3..3..3....1..1..3..3....0..0..2..2....0..0..3..3....3..3..3..3
%e A201216 ..1..2..3..2....2..2..2..3....0..3..2..3....2..2..2..3....1..1..2..3
%Y A201216 Column 1 is A200759
%K A201216 nonn,tabl
%O A201216 1,1
%A A201216 _R. H. Hardin_ Nov 28 2011