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%I #6 Nov 26 2014 10:56:14
%S 28456,190213,994030,4416061,17202711,60472234,195029867,584383121,
%T 1641320797,4350649060,10946535213,26264135834,60344532228,
%U 133238716551,283638236272,583811316064,1164928298365,2258673657000,4264498245386
%N Number of (n+1)X(6+1) 0..2 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction
%C Column 6 of A250632
%H R. H. Hardin, <a href="/A250630/b250630.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-1) -28*a(n-2) +12*a(n-3) +134*a(n-4) -294*a(n-5) -28*a(n-6) +876*a(n-7) -919*a(n-8) -833*a(n-9) +2312*a(n-10) -680*a(n-11) -2380*a(n-12) +2380*a(n-13) +680*a(n-14) -2312*a(n-15) +833*a(n-16) +919*a(n-17) -876*a(n-18) +28*a(n-19) +294*a(n-20) -134*a(n-21) -12*a(n-22) +28*a(n-23) -9*a(n-24) +a(n-25) for n>36
%F Empirical for n mod 2 = 0: a(n) = (677/10461394944000)*n^16 + (323/32691859200)*n^15 + (328303/523069747200)*n^14 + (23351/1067489280)*n^13 + (26884057/57480192000)*n^12 + (19162687/2874009600)*n^11 + (264304657/3657830400)*n^10 + (282962783/365783040)*n^9 + (546703353947/73156608000)*n^8 + (9006721609/261273600)*n^7 + (606619175047/2874009600)*n^6 + (5364465529/35925120)*n^5 + (1489177450559837/72648576000)*n^4 - (52712541330373/363242880)*n^3 + (55868420400113/100900800)*n^2 - (20512474811/60060)*n - 1864584 for n>11
%F Empirical for n mod 2 = 1: a(n) = (677/10461394944000)*n^16 + (323/32691859200)*n^15 + (328303/523069747200)*n^14 + (23351/1067489280)*n^13 + (26884057/57480192000)*n^12 + (19162687/2874009600)*n^11 + (264304657/3657830400)*n^10 + (282962783/365783040)*n^9 + (546703353947/73156608000)*n^8 + (9007343689/261273600)*n^7 + (607505328007/2874009600)*n^6 + (10667540267/71850240)*n^5 + (1489289213961587/72648576000)*n^4 - (422056644097481/2905943040)*n^3 + (1787002967118631/3228825600)*n^2 - (863144758907/2562560)*n - (3842277903/2048)for n>11
%e Some solutions for n=2
%e ..0..0..1..1..1..1..1....0..0..0..0..0..0..1....0..0..0..0..0..0..0
%e ..0..0..1..1..1..1..2....0..0..0..0..1..0..2....0..0..0..0..0..1..2
%e ..2..0..2..2..1..2..2....1..2..2..2..0..2..1....0..1..1..0..1..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 26 2014
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