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%I #6 Sep 08 2022 13:10:25
%S 10,14,87,427,1688,5726,18486,59458,189516,589078,1771979,5155016,
%T 14529474,39751677,105748979,273953703,692141498,1707798168,
%U 4120669743,9734318169,22538154434,51195509983,114191870360,250314850722
%N Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 4 array.
%C Column 4 of A219686.
%H R. H. Hardin, <a href="/A219682/b219682.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/8841761993739701954543616000000)*n^29 - (1/50814724101952310083584000000)*n^28 + (1/580739704022312115240960000)*n^27 - (1/53772194816880751411200000)*n^26 - (67/6768528018908066611200000)*n^25 + (4643/4136322678221596262400000)*n^24 - (1309733/24054307267196359802880000)*n^23 + (776987/2265985467199657082880000)*n^22 + (410911/2972563908172185600000)*n^21 - (490056821/49047304484841062400000)*n^20 + (16372002799/49801878399992463360000)*n^19 - (968981309/631017952436551680000)*n^18 - (17406895711696783/46512333274098224332800000)*n^17 + (8682271622870311/456003267393119846400000)*n^16 - (1074465658101893/2368848142301921280000)*n^15 + (12853594615136699/4342888260886855680000)*n^14 + (3714463850051933851/21296855894733619200000)*n^13 - (16329337796841689161/2366317321637068800000)*n^12 + (563272404080038801903/4456702186362961920000)*n^11 - (41790908888053128958991/38624752281812336640000)*n^10 - (2068970873910075110920537/379350245624942592000000)*n^9 + (12606404340006385030084357/42150027291660288000000)*n^8 - (2180783444974657064143769/497154168055480320000)*n^7 + (96109697881649790417637807/2692918410300518400000)*n^6 - (136580940782604083515955587/928240815671769600000)*n^5 - (1259605322569179919156739/12605739472085760000)*n^4 + (11723883931469901490135337/2431106898187968000)*n^3 - (25408893790340784114283/964724959598400)*n^2 + (5037095951528247967/77636318760)*n - 61265531 for n>13.
%e Some solutions for n=3
%e ..2..1..0..0....1..1..1..1....1..0..0..0....1..1..1..0....2..1..0..0
%e ..2..1..0..0....1..0..0..0....0..0..0..0....1..1..0..0....2..1..0..0
%e ..2..1..1..1....0..0..0..0....0..0..1..2....2..1..0..0....2..1..0..0
%Y Cf. A219686.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 25 2012
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