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%I #4 Nov 30 2014 18:08:48
%S 1728,7776,34992,157464,466560,1382400,4096000,9600000,22500000,
%T 52734375,106312500,214326000,432081216,784147392,1423082304,
%U 2582630848,4337012736,7283146752,12230590464,19349176320,30611001600,48427561125
%N Number of (n+2)X(2+2) 0..1 arrays with nondecreasing sum of every three consecutive values in every row and column
%C Column 2 of A251192
%H R. H. Hardin, <a href="/A251188/b251188.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) -a(n-2) +11*a(n-3) -22*a(n-4) +11*a(n-5) -55*a(n-6) +110*a(n-7) -55*a(n-8) +165*a(n-9) -330*a(n-10) +165*a(n-11) -330*a(n-12) +660*a(n-13) -330*a(n-14) +462*a(n-15) -924*a(n-16) +462*a(n-17) -462*a(n-18) +924*a(n-19) -462*a(n-20) +330*a(n-21) -660*a(n-22) +330*a(n-23) -165*a(n-24) +330*a(n-25) -165*a(n-26) +55*a(n-27) -110*a(n-28) +55*a(n-29) -11*a(n-30) +22*a(n-31) -11*a(n-32) +a(n-33) -2*a(n-34) +a(n-35)
%F Empirical for n mod 3 = 0: a(n) = (1/4251528)*n^12 + (23/1417176)*n^11 + (10/19683)*n^10 + (751/78732)*n^9 + (6277/52488)*n^8 + (6149/5832)*n^7 + (19537/2916)*n^6 + (15019/486)*n^5 + (2771/27)*n^4 + (6458/27)*n^3 + (3340/9)*n^2 + 344*n + 144
%F Empirical for n mod 3 = 1: a(n) = (1/4251528)*n^12 + (23/1417176)*n^11 + (181/354294)*n^10 + (10313/1062882)*n^9 + (29255/236196)*n^8 + (264475/236196)*n^7 + (2604875/354294)*n^6 + (4173125/118098)*n^5 + (58290625/472392)*n^4 + (1298328125/4251528)*n^3 + (90078125/177147)*n^2 + (90625000/177147)*n + (125000000/531441)
%F Empirical for n mod 3 = 2: a(n) = (1/4251528)*n^12 + (23/1417176)*n^11 + (10/19683)*n^10 + (20285/2125764)*n^9 + (56585/472392)*n^8 + (166723/157464)*n^7 + (4789069/708588)*n^6 + (1853920/59049)*n^5 + (2073820/19683)*n^4 + (132409760/531441)*n^3 + (69829312/177147)*n^2 + (2458624/6561)*n + (86051840/531441)
%e Some solutions for n=4
%e ..0..1..0..0....0..1..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..0..0..1..1....0..0..0..0....0..0..0..0....0..1..0..0....0..0..0..1
%e ..0..0..0..1....0..0..0..1....0..1..1..0....0..1..0..0....0..0..1..1
%e ..1..1..1..1....1..1..1..1....0..0..0..0....1..1..1..1....0..1..0..1
%e ..1..0..1..1....0..0..1..0....1..1..0..1....0..1..0..1....0..1..1..1
%e ..1..0..1..1....0..1..0..1....0..1..1..1....0..1..0..0....0..0..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2014
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