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A184573 Number of (n+2)X10 0..3 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A184573 #7 Jul 22 2025 09:38:21
%S A184573 318063303,9696377100,171891306894,2213469458762,22587829272879,
%T A184573 191432663548535,1389863286849772,8847094859463950,50288280003912690,
%U A184573 259097398200707061,1225103456113642803,5371748111324539632
%N A184573 Number of (n+2)X10 0..3 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A184573 Column 8 of A184574
%H A184573 R. H. Hardin, <a href="/A184573/b184573.txt">Table of n, a(n) for n = 1..200</a>
%F A184573 Empirical: a(n) = (673/181350051998613446979077070127104000000000)*n^40
%F A184573 + (965677/462442632596464289796646528824115200000000)*n^39
%F A184573 + (55869007/98247885313534537758994500629299200000000)*n^38
%F A184573 + (14692207/146742929700158271190532326686720000000)*n^37
%F A184573 + (1129481833003/88045757820094962714319396012032000000000)*n^36
%F A184573 + (35144498153879/27555061243696386479111070233395200000000)*n^35
%F A184573 + (25401235273163749/247995551193267478311999632100556800000000)*n^34
%F A184573 + (262126995417151/38389404209484129769659385774080000000)*n^33
%F A184573 + (3596914274137699/9332719339520164616768323584000000000)*n^32
%F A184573 + (539235358252563887/28829987350995986783538669158400000000)*n^31
%F A184573 + (1116387366983689356767/1411739380606835739916506444595200000000)*n^30
%F A184573 + (231485648220727758173/7842996558926865221758369136640000000)*n^29
%F A184573 + (2322340559452286223827/2351723106124997067993513984000000000)*n^28
%F A184573 + (81605062321920105148379/2704481572043746628192541081600000000)*n^27
%F A184573 + (16599486295341432111403/19317725514598190201375293440000000)*n^26
%F A184573 + (97625742346088765429/4211276194400103749910528000000)*n^25
%F A184573 + (174888755958896985910044011/293699356240044882699642470400000000)*n^24
%F A184573 + (88489208847914976941793254377/6130158229965825690569759784960000000)*n^23
%F A184573 + (896113550321153560129112114503/2762205684648632919861472788480000000)*n^22
%F A184573 + (2747951381674061199065405244271/414330852697294937979220918272000000)*n^21
%F A184573 + (8785427708895423890367179641428077/72343482216988005043990953984000000000)*n^20
%F A184573 + (23628790084724156964201017870485871/11993787841237485046766921318400000000)*n^19
%F A184573 + (23265331627981998133937028213755823239/827571361045386468226917570969600000000)*n^18
%F A184573 + (10553549822849284259060835463023491/30049795244930518091028234240000000)*n^17
%F A184573 + (38827441360182895772263834450498494341/10141805895164049855722029056000000000)*n^16
%F A184573 + (969627877078730019758713838729373991/26688962882010657515057971200000000)*n^15
%F A184573 + (21703826536213623030401303969738892503/72441470679743213255157350400000000)*n^14
%F A184573 + (4182327134423349818635798965138531349/1950347287531548049177313280000000)*n^13
%F A184573 + (353946924402717018399904311295348912463/26595644829975655216054272000000000)*n^12
%F A184573 + (137399484184209533572268883565100391029/1920796571053797321159475200000000)*n^11
%F A184573 + (6309671962132576848901067927195231043092297/18994757291151001708946050252800000000)*n^10
%F A184573 + (675760525354911330698025546025089536579/509789513986876052306657280000000)*n^9
%F A184573 + (141304268507668371503738345865177547189957/31406675415262899651035136000000000)*n^8
%F A184573 + (775423336961362770909286840964803808189/60711409590907814465126400000000)*n^7
%F A184573 + (4008183003568711530630026347248376762093/135412839652763951393955840000000)*n^6
%F A184573 + (938628647546903640486120815258199628913/17302751733408727122561024000000)*n^5
%F A184573 + (226211122595937892873492340247370663691/2996018342016338711123251200000)*n^4
%F A184573 + (216326320315708236509529777041751493/2873165738044769266619520000)*n^3
%F A184573 + (496967716499616196779836511031/10279294973506383552000)*n^2
%F A184573 + (759115441294391109931/48134517631200)*n
%F A184573 + 286599
%e A184573 Some solutions for 4X10
%e A184573 ..0..0..0..0..0..0..0..0..0..3....0..0..0..0..0..0..0..0..0..0
%e A184573 ..0..0..0..0..0..0..0..0..2..3....0..0..0..0..0..0..0..1..1..3
%e A184573 ..0..0..0..0..0..0..0..1..0..2....0..0..0..0..0..0..0..1..2..0
%e A184573 ..0..0..0..0..0..0..0..2..2..1....0..0..0..0..0..0..0..2..0..0
%K A184573 nonn
%O A184573 1,1
%A A184573 _R. H. Hardin_ Jan 17 2011