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A219591 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.

%I A219591 #6 Jul 23 2025 00:33:31
%S A219591 10,34,233,1114,4350,16117,60252,226309,831045,2932198,9899904,
%T A219591 32047091,99786646,299774977,871181292,2454943142,6722356023,
%U A219591 17921513868,46593529264,118305418513,293738371262,713963398966,1700512384149
%N A219591 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.
%C A219591 Column 4 of A219595
%H A219591 R. H. Hardin, <a href="/A219591/b219591.txt">Table of n, a(n) for n = 1..210</a>
%F A219591 Empirical: a(n) = (1/81868166608700944023552000000)*n^29 - (67/33876482734634873389056000000)*n^28 + (1093/7259246300278901440512000000)*n^27 - (1/940621483677214310400000)*n^26 - (47119/62044840173323943936000000)*n^25 + (1869449/24817936069329577574400000)*n^24 - (296052733/86862776242653521510400000)*n^23 + (54522829/1510656978133104721920000)*n^22 + (167845631/29428382690904637440000)*n^21 - (6024199483/14013515567097446400000)*n^20 + (8467657127141/539520349333251686400000)*n^19 - (2932958591041/11358323143857930240000)*n^18 - (12704169291856247/2584018515227679129600000)*n^17 + (47097728297965439/101334059420693299200000)*n^16 - (1011984217642567843/65143323913302835200000)*n^15 + (364057784069101777/1240825217396244480000)*n^14 - (56366476163066975107/28395807859644825600000)*n^13 - (904186645491855977543/14197903929822412800000)*n^12 + (6474020741492280364763/2600993419650662400000)*n^11 - (1166634295507637525043197/25749834854541557760000)*n^10 + (717109824273215889502078381/1517400982499770368000000)*n^9 - (6363461015557560073335283/4014288313491456000000)*n^8 - (11656748989007326967754487087/323150209236062208000000)*n^7 + (3938184473751556080945711017/5385836820601036800000)*n^6 - (163994244837799128753946400473/22690331049754368000000)*n^5 + (30438522365937746680601642677/680709931492631040000)*n^4 - (60274458996187160134975931/347300985455424000)*n^3 + (102759246483272304467447/275635702742400)*n^2 - (195156984499999649389/776363187600)*n - 310620487 for n>13
%e A219591 Some solutions for n=3
%e A219591 ..1..1..0..0....2..2..0..0....0..0..0..0....1..1..0..0....1..1..0..0
%e A219591 ..1..1..1..0....2..2..1..0....0..0..0..0....1..1..1..0....1..1..1..0
%e A219591 ..2..2..2..2....2..2..1..1....2..1..1..1....2..1..0..0....1..1..1..2
%K A219591 nonn
%O A219591 1,1
%A A219591 _R. H. Hardin_ Nov 23 2012