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%I #9 Nov 14 2018 09:33:13
%S 36,108,324,720,1600,3000,5625,9450,15876,24696,38416,56448,82944,
%T 116640,164025,222750,302500,399300,527076,679536,876096,1107288,
%U 1399489,1739010,2160900,2646000,3240000,3916800,4734976,5659776,6765201,8005878
%N Number of (n+1)X(2+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
%H R. H. Hardin, <a href="/A250426/b250426.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) - 5*a(n-4) + 20*a(n-5) - 20*a(n-7) + 5*a(n-8) + 10*a(n-9) - 4*a(n-10) - 2*a(n-11) + a(n-12).
%F Empirical for n mod 2 = 0: a(n) = (1/256)*n^6 + (11/128)*n^5 + (49/64)*n^4 + (113/32)*n^3 + (71/8)*n^2 + (23/2)*n + 6.
%F Empirical for n mod 2 = 1: a(n) = (1/256)*n^6 + (11/128)*n^5 + (199/256)*n^4 + (237/64)*n^3 + (2511/256)*n^2 + (1755/128)*n + (2025/256).
%F a(n+1)=A202093(n). - _R. J. Mathar_, Dec 04 2014
%F Empirical g.f.: x*(36 + 36*x - 36*x^2 + 124*x^4 - 20*x^5 - 115*x^6 + 40*x^7 + 56*x^8 - 26*x^9 - 11*x^10 + 6*x^11) / ((1 - x)^7*(1 + x)^5). - _Colin Barker_, Nov 14 2018
%e Some solutions for n=6:
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
%e ..0..1..0....0..0..0....0..0..1....0..0..1....0..0..0....0..1..0....0..0..1
%e ..0..1..1....0..0..0....0..0..1....0..0..0....0..0..1....0..1..0....0..1..1
%e ..0..1..1....0..0..0....0..0..1....0..1..1....0..0..1....0..1..0....0..0..1
%e ..0..1..1....0..0..0....0..0..1....0..0..1....0..1..1....0..1..0....0..1..1
%e ..1..1..1....0..1..1....0..1..1....1..1..1....1..1..1....0..1..1....0..0..1
%e ..0..1..1....0..1..1....0..1..1....1..0..1....1..1..1....1..1..1....1..1..1
%Y Column 2 of A250432.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 22 2014
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