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%I #8 Dec 02 2014 12:04:03
%S 400,3000,22500,105000,490000,1715000,6002500,17287200,49787136,
%T 124467840,311169600,698544000,1568160000,3234330000,6670805625,
%U 12847477500,24743290000,45032787800,81959673796,142244061960
%N Number of (n+1)X(6+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
%C Column 6 of A250432.
%H R. H. Hardin, <a href="/A250430/b250430.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +12*a(n-2) -26*a(n-3) -65*a(n-4) +156*a(n-5) +208*a(n-6) -572*a(n-7) -429*a(n-8) +1430*a(n-9) +572*a(n-10) -2574*a(n-11) -429*a(n-12) +3432*a(n-13) -3432*a(n-15) +429*a(n-16) +2574*a(n-17) -572*a(n-18) -1430*a(n-19) +429*a(n-20) +572*a(n-21) -208*a(n-22) -156*a(n-23) +65*a(n-24) +26*a(n-25) -12*a(n-26) -2*a(n-27) +a(n-28)
%F Empirical for n mod 2 = 0: a(n) = (1/339738624)*n^14 + (13/56623104)*n^13 + (697/84934656)*n^12 + (2521/14155776)*n^11 + (55639/21233664)*n^10 + (97807/3538944)*n^9 + (1143251/5308416)*n^8 + (1113683/884736)*n^7 + (1838411/331776)*n^6 + (505009/27648)*n^5 + (919427/20736)*n^4 + (265331/3456)*n^3 + (4297/48)*n^2 + (377/6)*n + 20
%F Empirical for n mod 2 = 1: a(n) = (1/339738624)*n^14 + (13/56623104)*n^13 + (2795/339738624)*n^12 + (5081/28311552)*n^11 + (301475/113246208)*n^10 + (178667/6291456)*n^9 + (76312715/339738624)*n^8 + (18940223/14155776)*n^7 + (2048631355/339738624)*n^6 + (1158380483/56623104)*n^5 + (647048923/12582912)*n^4 + (292086865/3145728)*n^3 + (477479275/4194304)*n^2 + (177888375/2097152)*n + (121550625/4194304).
%F a(n+1) = A202097(n). - _R. J. Mathar_, Dec 02 2014
%e Some solutions for n=4
%e ..0..0..1..1..1..1..1....0..0..0..1..1..1..1....0..0..0..0..0..0..1
%e ..0..0..1..0..1..1..1....0..1..0..1..0..1..1....0..0..0..1..0..1..0
%e ..1..0..1..1..1..1..1....1..0..1..1..1..1..1....0..1..1..1..1..1..1
%e ..0..0..1..1..1..1..1....0..1..0..1..1..1..1....0..0..0..1..0..1..0
%e ..1..0..1..1..1..1..1....1..1..1..1..1..1..1....0..1..1..1..1..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 22 2014
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