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A219688 Number of 4Xn 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 4Xn array.

%I A219688 #6 Jul 23 2025 00:36:36
%S A219688 10,19,99,427,1531,5031,15763,47784,140586,401745,1116450,3022129,
%T A219688 7979699,20573716,51835099,127704345,307858090,726741861,1681297548,
%U A219688 3815152314,8498764539,18601381870,40034714647,84794977698,176874740063
%N A219688 Number of 4Xn 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 4Xn array.
%C A219688 Row 4 of A219686
%H A219688 R. H. Hardin, <a href="/A219688/b219688.txt">Table of n, a(n) for n = 1..125</a>
%F A219688 Empirical: a(n) = (1/71811157608013824000000)*n^25 - (101/17234677825923317760000)*n^24 + (5449/4308669456480829440000)*n^23 - (68021/374666909259202560000)*n^22 + (9824237/510909421717094400000)*n^21 - (21583/13610640605184000)*n^20 + (5371647499/51090942171709440000)*n^19 - (394323599/68948639907840000)*n^18 + (45438295453/175751435059200000)*n^17 - (16515462281/1687213776568320)*n^16 + (542084002355513/1739939207086080000)*n^15 - (28192245777209/3381806039040000)*n^14 + (3250324207416831463/17399392070860800000)*n^13 - (1612171294329183241/463983788556288000)*n^12 + (2781152508058068181/52725430517760000)*n^11 - (757894220102779469/1198305239040000)*n^10 + (37334585059613913334793/6722492391014400000)*n^9 - (107120698751683891/3939922280448)*n^8 - (79214526965365782185939/798295971432960000)*n^7 + (49706772664271871813409/13646084981760000)*n^6 - (2005940155459581015843920483/48784753809792000000)*n^5 + (15777623834516738464154783/54205282010880000)*n^4 - (17331604984082844755616061/12467214862502400)*n^3 + (215362834119633956818141/49473074851200)*n^2 - (4207251609878775049/524924400)*n + 6438609162 for n>14
%e A219688 Some solutions for n=3
%e A219688 ..1..1..0....2..0..0....0..0..0....1..1..0....2..1..1....1..0..0....1..0..0
%e A219688 ..1..0..0....2..0..0....0..0..0....1..0..0....2..1..1....1..0..0....1..0..0
%e A219688 ..2..0..0....2..1..1....1..0..0....1..0..0....2..2..2....1..0..0....1..1..1
%e A219688 ..2..1..1....2..1..1....1..2..2....2..2..2....2..2..2....2..1..1....1..1..1
%K A219688 nonn
%O A219688 1,1
%A A219688 _R. H. Hardin_ Nov 25 2012