|
%I #4 Nov 29 2012 16:39:03
%S 10,33,218,1302,6367,28116,116212,452177,1661479,5791018,19242699,
%T 61244524,187461137,553667969,1582231440,4384799386,11806014470,
%U 30933256186,78981312321,196763074685,478829103169,1139452276535
%N Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array
%C Column 4 of A219852
%H R. H. Hardin, <a href="/A219848/b219848.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/4420880996869850977271808000000)*n^29 + (1/43555477801673408643072000000)*n^28 + (1/1209874383379816906752000000)*n^27 + (43/439954321229024329728000000)*n^26 + (239/46533630129992957952000000)*n^25 + (1271/10636258315426961817600000)*n^24 + (21559/2090280711721608806400000)*n^23 + (2358089/9711366287998530355200000)*n^22 + (414811/73570956727261593600000)*n^21 + (96602227/294283826909046374400000)*n^20 + (897677023/809280523999877529600000)*n^19 + (4533921193/24339263879695564800000)*n^18 + (931787469289/1162808331852455608320000)*n^17 + (164434612939/35532722134528819200000)*n^16 + (82237113442087/32571661956651417600000)*n^15 - (7016537322680609/130286647826605670400000)*n^14 + (695260733531027/704028294040780800000)*n^13 - (5073772635108677/6084815969923891200000)*n^12 - (507672575885083506979/2317485136908740198400000)*n^11 + (120144564891354934729/23647807519476940800000)*n^10 - (25084670412668166038597/505800327499923456000000)*n^9 + (11002475205125616793367/84300054583320576000000)*n^8 + (55130981973962294196913/19008835837415424000000)*n^7 - (13650131787757855786477/349729663675392000000)*n^6 + (44536807843513217954827921/204212979447789312000000)*n^5 - (23789530616592898876307/58346565556511232000)*n^4 - (1428365140707503731/767394854226000)*n^3 + (2161164468159204637/160787493266400)*n^2 - (27831547648057/840219900)*n + 31438 for n>7
%e Some solutions for n=3
%e ..1..1..1..1....1..0..0..0....0..0..0..0....1..1..1..1....1..1..0..0
%e ..1..1..0..0....1..0..0..0....0..0..0..0....1..1..1..1....1..1..0..0
%e ..1..1..0..2....1..1..0..0....0..0..0..0....1..1..1..2....2..1..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 29 2012
| 