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A185435 T(n,k)=Number of (n+2)X(k+2) 0..7 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A185435 #10 Jul 22 2025 09:46:58
%S A185435 6842284,284037544,284037544,8653394212,21536560306,8653394212,
%T A185435 212298419684,1090205284029,1090205284029,212298419684,4370405405266,
%U A185435 41910604337378,84722449466168,41910604337378,4370405405266
%N A185435 T(n,k)=Number of (n+2)X(k+2) 0..7 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A185435 Table starts
%C A185435 .............6842284..............284037544................8653394212
%C A185435 ...........284037544............21536560306.............1090205284029
%C A185435 ..........8653394212..........1090205284029............84722449466168
%C A185435 ........212298419684.........41910604337378..........4772160687307074
%C A185435 .......4370405405266.......1297535366114472........209290512833668811
%C A185435 ......77657199293322......33575010264022917.......7468756070356586903
%C A185435 ....1216284173329482.....745543958045415621.....223694029250999654095
%C A185435 ...17062128865116751...14492443009379677098....5755145891541173071730
%C A185435 ..217083576402029968..250496452202647761530..129520045203909930078682
%C A185435 .2530473438240068012.3898612401674733619729.2587203198419699686906895
%H A185435 R. H. Hardin, <a href="/A185435/b185435.txt">Table of n, a(n) for n = 1..83</a>
%H A185435 R. H. Hardin, <a href="/A185435/a185435.txt">Polynomials for columns 1-3</a>
%F A185435 Empirical: T(n,k) is a polynomial of degree 7k+112, for fixed k
%F A185435 Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
%F A185435 Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.
%e A185435 Some solutions for 5X4
%e A185435 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A185435 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A185435 ..0..0..0..0....0..0..0..4....0..0..0..0....0..0..0..0....0..0..0..4
%e A185435 ..0..1..1..2....0..0..2..3....0..1..4..5....0..0..5..6....0..0..6..7
%e A185435 ..0..3..7..3....0..7..0..5....0..2..1..6....2..2..6..4....0..4..3..0
%K A185435 nonn,tabl
%O A185435 1,1
%A A185435 _R. H. Hardin_, General degree formula intuited by _D. S. McNeil_ in the Sequence Fans Mailing List, Jan 27 2011