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A185477 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A185477 #11 Jul 22 2025 09:48:41
%S A185477 1169,4594,4594,13659,21834,13659,34779,76309,76309,34779,79743,
%T A185477 225672,308692,225672,79743,169052,594798,1043186,1043186,594798,
%U A185477 169052,336690,1433903,3097348,3959167,3097348,1433903,336690,636698,3212372,8297059
%N A185477 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A185477 Table starts
%C A185477 ....1169.....4594.....13659......34779......79743......169052.......336690
%C A185477 ....4594....21834.....76309.....225672.....594798.....1433903......3212372
%C A185477 ...13659....76309....308692....1043186....3097348.....8297059.....20411234
%C A185477 ...34779...225672...1043186....3959167...12990375....37961900....100908633
%C A185477 ...79743...594798...3097348...12990375...46410729...146203201....416227164
%C A185477 ..169052..1433903...8297059...37961900..146203201...493061605...1497314456
%C A185477 ..336690..3212372..20411234..100908633..416227164..1497314456...4845252741
%C A185477 ..636698..6763143..46732687..247920339.1090826214..4179700035..14425457557
%C A185477 .1151966.13496424.100636591..570069808.2669230399.10893560939..40183952539
%C A185477 .2005704.25706057.205574323.1239033996.6166331968.26828743607.106069534256
%H A185477 R. H. Hardin, <a href="/A185477/b185477.txt">Table of n, a(n) for n = 1..1404</a>
%H A185477 R. H. Hardin, <a href="/A185477/a185477.txt">Polynomials for columns 1-8</a>
%F A185477 Empirical: T(n,k) is a polynomial of degree 2k+7 in n, for fixed k.
%F A185477 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 A185477 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 A185477 Some solutions for 5X4
%e A185477 ..0..0..0..0....0..0..1..1....0..0..0..1....0..0..0..2....0..0..0..1
%e A185477 ..0..0..0..2....1..1..1..2....0..0..0..1....1..1..1..2....0..0..1..2
%e A185477 ..0..0..1..2....1..1..1..2....0..0..0..1....1..1..1..2....0..1..2..2
%e A185477 ..0..1..1..2....1..1..2..1....1..1..2..1....1..1..1..2....0..2..0..0
%e A185477 ..2..1..1..2....1..2..0..2....2..2..1..0....1..1..2..2....0..2..2..2
%K A185477 nonn,tabl
%O A185477 1,1
%A A185477 _R. H. Hardin_, General degree formula intuited by _D. S. McNeil_ in the Sequence Fans Mailing List, Jan 28 2011