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A219597 Number of 4Xn 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 4Xn array.

%I A219597 #6 Jul 23 2025 00:34:11
%S A219597 10,46,264,1114,4152,14793,51122,170728,550156,1714425,5181670,
%T A219597 15217623,43453991,120646669,325663378,854806408,2182941966,
%U A219597 5428211529,13157408701,31124038143,71939605189,162674579688,360302418944
%N A219597 Number of 4Xn 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 4Xn array.
%C A219597 Row 4 of A219595
%H A219597 R. H. Hardin, <a href="/A219597/b219597.txt">Table of n, a(n) for n = 1..143</a>
%F A219597 Empirical: a(n) = (1/32315020923606220800000)*n^25 - (109/11079435745236418560000)*n^24 + (2143/1292600836944248832000)*n^23 - (79003/421500272916602880000)*n^22 + (50173/3193183885731840000)*n^21 - (44960737/43792236147179520000)*n^20 + (27515689/510909421717094400)*n^19 - (60384781/26191528796160000)*n^18 + (21813448039/268899695640576000)*n^17 - (2221068910103/949057749319680000)*n^16 + (9482825036023/173993920708608000)*n^15 - (91557547148539/93211028951040000)*n^14 + (5251971236010727/434984801771520000)*n^13 - (62481716542887379/1491376463216640000)*n^12 - (9282784846386031/3954407288832000)*n^11 + (4293029543793101017/59316109332480000)*n^10 - (105931313393469849253/84031154887680000)*n^9 + (202993929290792591407/13095764398080000)*n^8 - (3712306914099958615759/26609865714432000)*n^7 + (11336104215245400553903/12671364625920000)*n^6 - (369076146776783247776693/101634903770400000)*n^5 + (41196192835097343490679/9034213668480000)*n^4 + (15522433799255326230017/346311523958400)*n^3 - (23040269972514059058427/74209612276800)*n^2 + (112252070661045629/127481640)*n - 1011429662 for n>12
%e A219597 Some solutions for n=3
%e A219597 ..0..0..0....0..0..0....1..0..0....0..0..0....1..0..0....0..0..0....0..0..0
%e A219597 ..0..0..0....1..0..0....1..0..0....1..0..0....0..0..0....2..0..0....1..0..0
%e A219597 ..0..0..0....0..0..0....1..1..0....1..1..0....2..0..0....2..1..0....1..0..0
%e A219597 ..1..1..0....0..0..0....1..1..2....1..2..2....2..2..1....2..1..1....1..1..0
%K A219597 nonn
%O A219597 1,1
%A A219597 _R. H. Hardin_ Nov 23 2012