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A220149 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.

%I A220149 #6 Jul 23 2025 00:53:35
%S A220149 10,50,254,1174,5410,24684,108169,448881,1761976,6564622,23314449,
%T A220149 79243936,258638752,812875058,2465906695,7234818015,20565976895,
%U A220149 56733702403,152106586332,396892051129,1009207780356,2503839951948
%N A220149 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.
%C A220149 Column 4 of A220153
%H A220149 R. H. Hardin, <a href="/A220149/b220149.txt">Table of n, a(n) for n = 1..210</a>
%F A220149 Empirical: a(n) = (1/552610124608731372158976000000)*n^29 + (1/7622208615292846512537600000)*n^28 + (1/272221736260458804019200000)*n^27 + (1/1878686930714001408000000)*n^26 + (463/23266815064996478976000000)*n^25 + (127/372269041039943663616000)*n^24 + (97193/2443015581824630292480000)*n^23 + (1458253/2124361375499678515200000)*n^22 + (293509/55178217545446195200000)*n^21 + (1203901/1051013667532308480000)*n^20 + (19197187/20232013099996938240000)*n^19 - (215771663/10648427947366809600000)*n^18 + (47996570583761/2907020829631139020800000)*n^17 - (3130777943459/13680098021793595392000)*n^16 + (352784890291/174491046196346880000)*n^15 + (12242591085947/145409205163622400000)*n^14 - (2308802430337703/1064842794736680960000)*n^13 + (63970460933829533/2129685589473361920000)*n^12 - (7607446827742849/82297057418634240000)*n^11 - (845289139000912665797/289685642113592524800000)*n^10 + (16663286001178049022791/284512684218706944000000)*n^9 - (300232887874952342719/602143247023718400000)*n^8 + (10527514392059792417183/6059066423176166400000)*n^7 + (113898768509462767685501/13464592051502592000000)*n^6 - (19927257308688059839763/149570053306486312500)*n^5 + (32438984170527374840711/44394125966910720000)*n^4 - (955894333256214244573/455832543410244000)*n^3 + (2762815941001472611/964724959598400)*n^2 - (432088153285363/1164544781400)*n - 2315 for n>4
%e A220149 Some solutions for n=3
%e A220149 ..0..0..0..0....2..2..0..0....2..1..0..1....1..0..0..1....1..1..0..1
%e A220149 ..2..2..0..0....2..2..2..2....2..2..0..0....2..0..0..0....1..1..0..0
%e A220149 ..2..2..2..2....2..2..2..2....2..2..2..2....2..2..1..0....2..2..0..0
%K A220149 nonn
%O A220149 1,1
%A A220149 _R. H. Hardin_ Dec 06 2012