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A220156 Number of 4Xn 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 4Xn array.

%I A220156 #6 Jul 23 2025 00:54:09
%S A220156 15,52,242,1174,4559,16110,53947,173732,539903,1620236,4698464,
%T A220156 13180052,35802185,94277039,240952485,598495844,1446788180,3408685943,
%U A220156 7838407335,17616947657,38749982170,83520468048,176604065342,366743870453
%N A220156 Number of 4Xn 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 4Xn array.
%C A220156 Row 4 of A220153
%H A220156 R. H. Hardin, <a href="/A220156/b220156.txt">Table of n, a(n) for n = 1..121</a>
%F A220156 Empirical: a(n) = (1/969450627708186624000000)*n^25 - (1/4562120600979701760000)*n^24 + (2027/77556050216654929920000)*n^23 - (331/177473799122780160000)*n^22 + (5539/80669908692172800000)*n^21 + (5921/3128016867655680000)*n^20 - (18577907/38318206628782080000)*n^19 + (18754471/474528874659840000)*n^18 - (41570691557/20167477173043200000)*n^17 + (5382522617/73004442255360000)*n^16 - (17042278220257/10439635242516480000)*n^15 + (9851672121271/1491376463216640000)*n^14 + (58162480943607049/52198176212582400000)*n^13 - (135094442095532831/2609908810629120000)*n^12 + (635574550376155319/474528874659840000)*n^11 - (1347751237421517133/59316109332480000)*n^10 + (296554709147396003149/1260467323315200000)*n^9 - (2610520959289132961/4236864952320000)*n^8 - (80984035976231237377421/3193183885731840000)*n^7 + (22349422485612993076363/44349776190720000)*n^6 - (7737663764129137016063569/1524523556556000000)*n^5 + (3378006014145622282711/109727291520000)*n^4 - (83444980373091022514603/820211504112000)*n^3 + (294465474881972180993/4365271310400)*n^2 + (987245448964903837/1487285800)*n - 1630947583 for n>18
%e A220156 Some solutions for n=3
%e A220156 ..0..0..0....1..0..0....1..0..0....0..0..0....0..0..0....1..0..0....1..1..1
%e A220156 ..1..0..0....1..0..0....1..0..0....1..0..0....0..0..0....2..0..0....1..0..1
%e A220156 ..1..1..1....2..0..0....2..0..0....1..1..2....1..1..0....2..1..1....1..0..0
%e A220156 ..2..2..1....2..0..0....2..1..1....1..1..1....1..1..1....2..2..2....1..1..1
%K A220156 nonn
%O A220156 1,1
%A A220156 _R. H. Hardin_ Dec 06 2012