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A185472 Number of (n+2)X6 0..2 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A185472 #7 Jul 22 2025 09:48:11
%S A185472 34779,225672,1043186,3959167,12990375,37961900,100908633,247920339,
%T A185472 570069808,1239033996,2565887950,5095678058,9756244258,18087995239,
%U A185472 32592776835,57255685167,98315034745,165384433476,273069215898
%N A185472 Number of (n+2)X6 0..2 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A185472 Column 4 of A185477
%H A185472 R. H. Hardin, <a href="/A185472/b185472.txt">Table of n, a(n) for n = 1..200</a>
%F A185472 Empirical: a(n) = (1/27243216000)*n^15
%F A185472 + (97/21794572800)*n^14
%F A185472 + (1549/6227020800)*n^13
%F A185472 + (4127/479001600)*n^12
%F A185472 + (676031/2395008000)*n^11
%F A185472 + (54763/6220800)*n^10
%F A185472 + (60678553/304819200)*n^9
%F A185472 + (904333037/304819200)*n^8
%F A185472 + (910283537/31104000)*n^7
%F A185472 + (8446896821/43545600)*n^6
%F A185472 + (213392977159/239500800)*n^5
%F A185472 + (52396736149/17107200)*n^4
%F A185472 + (70560211894163/9081072000)*n^3
%F A185472 + (1840763445463/151351200)*n^2
%F A185472 + (1738288907/180180)*n
%F A185472 + 1019
%e A185472 Some solutions for 4X6
%e A185472 ..0..0..0..1..1..1....0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..0
%e A185472 ..0..0..0..1..1..2....0..0..0..0..1..2....0..0..0..0..1..2....0..0..0..0..1..2
%e A185472 ..0..1..1..1..2..0....0..0..0..1..2..2....0..0..0..0..1..2....0..0..0..1..0..0
%e A185472 ..0..1..1..2..0..0....0..2..2..2..2..2....0..0..2..2..2..2....0..1..2..1..0..1
%K A185472 nonn
%O A185472 1,1
%A A185472 _R. H. Hardin_ Jan 28 2011