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A219473 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 3Xn array.

%I A219473 #6 Jul 23 2025 00:30:15
%S A219473 20,82,673,4838,28159,143718,674954,2941342,11981143,45898940,
%T A219473 166443227,574474013,1895549798,6001932167,18298398284,53884690148,
%U A219473 153709998598,425853237243,1148567805278,3022012284611,7771027231688,19561835095982
%N A219473 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 3Xn array.
%C A219473 Row 3 of A219471
%H A219473 R. H. Hardin, <a href="/A219473/b219473.txt">Table of n, a(n) for n = 1..210</a>
%F A219473 Empirical: a(n) = (1/523022617466601111760007224100074291200000000)*n^38 + (1/1448816114865931057506945219113779200000000)*n^37 + (1/21256761530851498141028539894333440000000)*n^36 - (757/247995551193267478311999632100556800000000)*n^35 + (4093/17713967942376248450857116578611200000000)*n^34 + (22907/520999057128713189731091664076800000000)*n^33 - (16139/7957076508874892352256672687718400000)*n^32 + (83764319/994634563609361544032084085964800000000)*n^31 + (549239/75761477976110107326205132800000000)*n^30 - (4678856243/7129996871751695656143971942400000000)*n^29 + (1496226007/25756967352797586935167057920000000)*n^28 - (653413544957/386354510291963804027505868800000000)*n^27 - (2975183387963/50709029475820249278610145280000000)*n^26 + (8806918400800111/811344471613123988457762324480000000)*n^25 - (11812904513950811/23181270617517828241650352128000000)*n^24 + (2067239075526283159/270448157204374662819254108160000000)*n^23 + (5489678448341620139/10384231897175311728802529280000000)*n^22 - (392659222400328327701/10384231897175311728802529280000000)*n^21 + (247423891090169051135981/225998646925797238897756864512000000)*n^20 - (1259752365431022645311581/654206609522044638914559344640000000)*n^19 - (2990270427949071173313147319/2570097394550889652878625996800000000)*n^18 + (1113341390309813951403492457/22047404119921847512439193600000000)*n^17 - (27170930857420612653952304299/28976588271897285302062940160000000)*n^16 - (271137930058645412943527770259/72441470679743213255157350400000000)*n^15 + (535219246244278434476862762431287/760635442137303739179152179200000000)*n^14 - (465297657459368886898913689163269/23769857566790741849348505600000000)*n^13 + (2384764688539478823620118815171/8980347604926844618407936000000)*n^12 - (1530415339594431692136387618041231/1920796571053797321159475200000000)*n^11 - (1852126074867674150037947762929883/51672635028348907526553600000000)*n^10 + (3777985100569138597814021070434363/6140112495652570801766400000000)*n^9 - (18055084608276660939474085529912310323/8793869116273611902289838080000000)*n^8 - (16027148120397118317452245023651668567/229007008236291976622131200000000)*n^7 + (146244839212731141496087089326560146347/111231975429056102930749440000000)*n^6 - (2021853520308780547462644486264447863/173027517334087271225610240000)*n^5 + (1473180274572635724831497308125294809/24718216762012467317944320000)*n^4 - (1282315843815358503748361492528617/8174013479501477287680000)*n^3 + (79251015920672692584467011831459/1243794691794272409792000)*n^2 + (221377469245024941019907/356195430470880)*n - 919752513 for n>16
%e A219473 Some solutions for n=3
%e A219473 ..0..0..2....1..1..2....0..0..0....0..0..0....0..0..0....0..0..0....0..0..2
%e A219473 ..0..0..1....1..1..2....0..0..2....0..1..3....0..0..2....0..2..2....1..1..1
%e A219473 ..0..0..1....3..2..3....3..2..2....3..0..0....2..2..2....3..2..2....3..1..1
%K A219473 nonn
%O A219473 1,1
%A A219473 _R. H. Hardin_ Nov 20 2012