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A219879 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.

%I A219879 #6 Jul 23 2025 00:45:32
%S A219879 10,17,129,621,2645,10350,40239,155199,581728,2085519,7121374,
%T A219879 23225035,72683520,219218974,639377404,1808073511,4967931875,
%U A219879 13286469360,34640551307,88162618939,219292820124,533661457600,1271821824645
%N A219879 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.
%C A219879 Column 4 of A219883
%H A219879 R. H. Hardin, <a href="/A219879/b219879.txt">Table of n, a(n) for n = 1..210</a>
%F A219879 Empirical: a(n) = (1/1105220249217462744317952000000)*n^29 + (1/38111043076464232562688000000)*n^28 - (1/201645730563302817792000000)*n^27 + (389/604937191689908453376000000)*n^26 - (307/46533630129992957952000000)*n^25 - (773/404640261999938764800000)*n^24 + (40878821/195441246545970423398400000)*n^23 - (70069501/8497445501998714060800000)*n^22 + (12139/477733485241958400000)*n^21 + (50109247/2829652181817753600000)*n^20 - (445566582679/404640261999938764800000)*n^19 + (737417025883/21296855894733619200000)*n^18 - (2216933583028729/5814041659262278041600000)*n^17 - (6268242075250621/342002450544839884800000)*n^16 + (18619463335254179/16285830978325708800000)*n^15 - (536852810288080877/16285830978325708800000)*n^14 + (1152350125136381123/2129685589473361920000)*n^13 - (24885562289413355029/10648427947366809600000)*n^12 - (39408208806540972298007/289685642113592524800000)*n^11 + (1255759711529881816639841/289685642113592524800000)*n^10 - (4460229918485515193847251/63225040937490432000000)*n^9 + (370772167856232917329483/540384965277696000000)*n^8 - (39409170362295331975190999/13464592051502592000000)*n^7 - (280106596148918041437854963/13464592051502592000000)*n^6 + (23189350672718808866722526453/51053244861947328000000)*n^5 - (379821968293133120568499603/102106489723894656000)*n^4 + (3496996713409130344932041/202592241515664000)*n^3 - (3708578246594560887479/83889126921600)*n^2 + (35941859372224430069/776363187600)*n + 10128532 for n>12
%e A219879 Some solutions for n=3
%e A219879 ..1..0..0..0....0..0..0..0....2..0..0..0....1..1..0..1....2..1..1..1
%e A219879 ..1..0..0..0....0..0..0..0....2..0..0..0....1..0..0..0....2..1..1..1
%e A219879 ..1..1..0..0....1..1..0..1....2..2..0..2....1..0..0..0....2..2..1..1
%K A219879 nonn
%O A219879 1,1
%A A219879 _R. H. Hardin_ Nov 30 2012