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%I #6 Dec 04 2014 13:14:31
%S 144,720,3600,12000,40000,105000,275625,617400,1382976,2765952,
%T 5531904,10160640,18662400,32076000,55130625,89842500,146410000,
%U 228399600,356303376,535927392,806105664,1175570760,1714374025,2434614000
%N Number of (n+1)X(4+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
%C Column 4 of A250432
%H R. H. Hardin, <a href="/A250428/b250428.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +8*a(n-2) -18*a(n-3) -27*a(n-4) +72*a(n-5) +48*a(n-6) -168*a(n-7) -42*a(n-8) +252*a(n-9) -252*a(n-11) +42*a(n-12) +168*a(n-13) -48*a(n-14) -72*a(n-15) +27*a(n-16) +18*a(n-17) -8*a(n-18) -2*a(n-19) +a(n-20)
%F Empirical for n mod 2 = 0: a(n) = (1/147456)*n^10 + (23/73728)*n^9 + (13/2048)*n^8 + (77/1024)*n^7 + (1763/3072)*n^6 + (4525/1536)*n^5 + (5927/576)*n^4 + (3473/144)*n^3 + (145/4)*n^2 + (63/2)*n + 12
%F Empirical for n mod 2 = 1: a(n) = (1/147456)*n^10 + (23/73728)*n^9 + (941/147456)*n^8 + (1409/18432)*n^7 + (43777/73728)*n^6 + (115189/36864)*n^5 + (831857/73728)*n^4 + (169595/6144)*n^3 + (717525/16384)*n^2 + (333375/8192)*n + (275625/16384).
%F a(n+1)=A202095(n). - _R. J. Mathar_, Dec 04 2014
%e Some solutions for n=6
%e ..0..0..0..1..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..0..1....0..0..0..1..0....0..1..0..1..1....0..0..0..1..1
%e ..0..0..1..1..1....0..0..0..1..0....0..0..0..0..0....0..0..1..0..1
%e ..0..1..0..1..1....0..0..0..1..1....1..1..1..1..1....0..1..0..1..1
%e ..1..0..1..1..1....0..1..0..1..1....0..0..1..0..1....1..0..1..0..1
%e ..1..1..1..1..1....0..0..0..1..1....1..1..1..1..1....0..1..1..1..1
%e ..1..1..1..1..1....0..1..0..1..1....0..0..1..1..1....1..0..1..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 22 2014
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