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A219466 Number of nX3 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 nX3 array.

%I A219466 #6 Jul 23 2025 00:29:37
%S A219466 10,68,673,5040,32229,185800,982456,4815782,22059734,95049799,
%T A219466 387398157,1500899485,5551333536,19675267097,67041131529,220243855894,
%U A219466 699365511947,2151361250171,6423848162633,18651881494908,52745972542258
%N A219466 Number of nX3 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 nX3 array.
%C A219466 Column 3 of A219471
%H A219466 R. H. Hardin, <a href="/A219466/b219466.txt">Table of n, a(n) for n = 1..210</a>
%F A219466 Empirical: a(n) = (1/523022617466601111760007224100074291200000000)*n^38 + (1/887984070401699680407482553650380800000000)*n^37 + (211/743986653579802434935998896301670400000000)*n^36 + (37/901802004339154466589089571274752000000)*n^35 + (23431/5904655980792082816952372192870400000000)*n^34 + (751/2566497818368045269611288985600000000)*n^33 + (18234521/994634563609361544032084085964800000000)*n^32 + (1202479/1177082323798060998854537379840000000)*n^31 + (3257916313/64169971845765260905295747481600000000)*n^30 + (15998577713/7129996871751695656143971942400000000)*n^29 + (34241128937/386354510291963804027505868800000000)*n^28 + (35548456637/11038700294056108686500167680000000)*n^27 + (10947288367751/101418058951640498557220290560000000)*n^26 + (237907312593869/73758588328465817132523847680000000)*n^25 + (71600877671657743/811344471613123988457762324480000000)*n^24 + (122707098285448223/54089631440874932563850821632000000)*n^23 + (3671970390070217/70641033314117766862602240000000)*n^22 + (1589133646897620433/1483461699596473104114647040000000)*n^21 + (264925397893974283417499/12429925580918848139376627548160000000)*n^20 + (3615125506802045691703/10064717069569917521762451456000000)*n^19 + (99834558409326312420878167/17990681761856227570150381977600000000)*n^18 + (8082599270771039606958097/88189616479687390049756774400000000)*n^17 + (40084616932042931244243721/48294313786495475503438233600000000)*n^16 + (82210406612645728578527/5375990402949403581087744000000)*n^15 + (77521233231877746972047550487/760635442137303739179152179200000000)*n^14 + (318314789653271743306315093267/190158860534325934794788044800000000)*n^13 - (158292888536859409403815888861/17287169139484175890435276800000000)*n^12 + (70868942634763610614565096827/128053104736919821410631680000000)*n^11 - (28239949688137362945250580263751/3978792897182865879544627200000000)*n^10 + (1250965614347251807731812019833/15788860703106610633113600000000)*n^9 - (23380069818927909043317980888257301/43969345581368059511449190400000000)*n^8 + (1533222352111813385357485885877/454604482851199953592320000000)*n^7 - (2368130301559082421877403072112469/97327978500424090064405760000000)*n^6 + (1758899229989365280437101191329/9040100174194737263616000000)*n^5 - (28115613360169956438589192637861/24718216762012467317944320000)*n^4 + (20392529937699678379400434687/4904408087700886372608000)*n^3 - (1495340558417657393233035721/177684955970610344256000)*n^2 + (3623955459298340527/485721041551200)*n - 732 for n>5
%e A219466 Some solutions for n=3
%e A219466 ..1..1..1....0..0..1....0..0..2....0..0..1....0..0..1....0..0..0....0..0..0
%e A219466 ..1..1..2....1..1..2....0..0..0....0..0..2....0..0..3....0..0..3....0..0..3
%e A219466 ..2..2..2....3..0..0....3..0..2....2..2..2....2..2..3....2..1..1....1..0..0
%K A219466 nonn
%O A219466 1,1
%A A219466 _R. H. Hardin_ Nov 20 2012