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%I #6 Nov 26 2014 10:56:52
%S 101308,720347,3951204,18465586,75537881,280151655,955747123,
%T 3044656152,9115002626,25819633391,69479042412,178359097164,
%U 438217013076,1033845362914,2348714299334,5152340057777,10940886068027,22541522631593
%N Number of (n+1)X(7+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 7 of A250632
%H R. H. Hardin, <a href="/A250631/b250631.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 10*a(n-1) -36*a(n-2) +30*a(n-3) +159*a(n-4) -468*a(n-5) +144*a(n-6) +1332*a(n-7) -2061*a(n-8) -818*a(n-9) +4940*a(n-10) -3078*a(n-11) -4845*a(n-12) +7752*a(n-13) -7752*a(n-15) +4845*a(n-16) +3078*a(n-17) -4940*a(n-18) +818*a(n-19) +2061*a(n-20) -1332*a(n-21) -144*a(n-22) +468*a(n-23) -159*a(n-24) -30*a(n-25) +36*a(n-26) -10*a(n-27) +a(n-28) for n>43
%F Empirical for n mod 2 = 0: a(n) = (577/800296713216000)*n^18 + (20899/177843714048000)*n^17 + (542519/62768369664000)*n^16 + (100621/261534873600)*n^15 + (25919287/2241727488000)*n^14 + (178221971/747242496000)*n^13 + (24701832019/7242504192000)*n^12 + (541110839/13412044800)*n^11 + (679371383/1714608000)*n^10 + (329713379797/73156608000)*n^9 + (25314812061317/689762304000)*n^8 - (465116928863/5748019200)*n^7 + (98835922126461937/23538138624000)*n^6 - (23816639361362957/653837184000)*n^5 + (686742376841666357/1307674368000)*n^4 - (3323571809548409/726485760)*n^3 + (96507695224350161/4410806400)*n^2 - (449398771514761/12252240)*n - 34958956 for n>15
%F Empirical for n mod 2 = 1: a(n) = (577/800296713216000)*n^18 + (20899/177843714048000)*n^17 + (542519/62768369664000)*n^16 + (100621/261534873600)*n^15 + (25919287/2241727488000)*n^14 + (178221971/747242496000)*n^13 + (24701832019/7242504192000)*n^12 + (541110839/13412044800)*n^11 + (679371383/1714608000)*n^10 + (329713379797/73156608000)*n^9 + (25313580342917/689762304000)*n^8 - (464862031583/5748019200)*n^7 + (98811764885754337/23538138624000)*n^6 - (23817024512329157/653837184000)*n^5 + (343269827843477641/653837184000)*n^4 - (13297605524145617/2905943040)*n^3 + (772655875710930793/35286451200)*n^2 - (28810788818068891/784143360)*n - (17931508195/512) for n>15
%e Some solutions for n=1
%e ..0..0..0..0..1..0..0..0....0..0..0..0..0..1..1..2....0..0..0..1..1..1..1..1
%e ..0..0..2..1..0..2..1..0....1..1..1..1..1..2..2..1....2..1..0..1..1..1..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 26 2014
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