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A186089 Number of (n+2)X4 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A186089 #7 Jul 22 2025 10:14:12
%S A186089 1252889,22559052,280102672,2743553694,22408644868,157927508610,
%T A186089 983600385660,5510351270895,28148281162513,132536596243411,
%U A186089 580315278868317,2380269230618654,9202746397302837,33716548041703337
%N A186089 Number of (n+2)X4 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A186089 Column 2 of A186096
%H A186089 R. H. Hardin, <a href="/A186089/b186089.txt">Table of n, a(n) for n = 1..200</a>
%F A186089 Empirical: a(n) = (1/1037743288624208555079379412896972800000000)*n^38
%F A186089 + (9587/13763753091226345046315979581580902400000000)*n^37
%F A186089 + (28529/33817575162718292497090858922803200000000)*n^36
%F A186089 + (50210497/123997775596633739155999816050278400000000)*n^35
%F A186089 + (1900280537/17713967942376248450857116578611200000000)*n^34
%F A186089 + (9810978167/520999057128713189731091664076800000000)*n^33
%F A186089 + (57089921089/23681775324032417715049621094400000000)*n^32
%F A186089 + (4087992351929/17148871786368302483311794585600000000)*n^31
%F A186089 + (303453087639563/16042492961441315226323936870400000000)*n^30
%F A186089 + (4412111988180881/3564998435875847828071985971200000000)*n^29
%F A186089 + (1012607727773101/14859788857383223231827148800000000)*n^28
%F A186089 + (619636013553448457/193177255145981902013752934400000000)*n^27
%F A186089 + (458949578768601001/3512313729926943672977326080000000)*n^26
%F A186089 + (943289164621422777259/202836117903280997114440581120000000)*n^25
%F A186089 + (59070867116817962298787/405672235806561994228881162240000000)*n^24
%F A186089 + (1393933770239512745891/345841633253676039410810880000000)*n^23
%F A186089 + (64202052337199276920051/649014493573456983050158080000000)*n^22
%F A186089 + (11193762585634106524077107/5192115948587655864401264640000000)*n^21
%F A186089 + (1372508760873429144032358479/32883401007721820474541342720000000)*n^20
%F A186089 + (234715009337204557947402530761/327103304761022319457279672320000000)*n^19
%F A186089 + (196919620544266318182437509750193/17990681761856227570150381977600000000)*n^18
%F A186089 + (26104076532588252567987652718051/176379232959374780099513548800000000)*n^17
%F A186089 + (897593478835185195052329498839/506583711047155337448652800000000)*n^16
%F A186089 + (339711053666750838203318321424907/18110367669935803313789337600000000)*n^15
%F A186089 + (6349701573494460077791558378539673/36220735339871606627578675200000000)*n^14
%F A186089 + (548749037509303811220820318146454901/380317721068651869589576089600000000)*n^13
%F A186089 + (45039178838637375189325633152939223/4321792284871043972608819200000000)*n^12
%F A186089 + (63110030791198126365586351934048441/960398285526898660579737600000000)*n^11
%F A186089 + (1429109394382916914750784172458483471/3978792897182865879544627200000000)*n^10
%F A186089 + (124266834396427914505767245501957821/73681349947830849621196800000000)*n^9
%F A186089 + (10567048538735385404340116838466697759/1570333770763144982551756800000000)*n^8
%F A186089 + (2427874275387519655050037351600570741/107768003875902106645708800000000)*n^7
%F A186089 + (8832810953454457317486336954522298211/141567968727889585548226560000000)*n^6
%F A186089 + (485730805911773470277068599637126553/3460550346681745424512204800000)*n^5
%F A186089 + (324665650575170794206768040559/1305907478973608797440000)*n^4
%F A186089 + (92093319388923975529326424091/281862533775913009920000)*n^3
%F A186089 + (1599179967649434547569863507/5552654874081573258000)*n^2
%F A186089 + (8435127242640643/58220894160)*n
%F A186089 + 10524
%e A186089 Some solutions for 6X4
%e A186089 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A186089 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A186089 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A186089 ..0..0..0..2....0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..2
%e A186089 ..0..1..1..4....1..1..3..2....2..3..4..3....3..3..0..2....0..1..2..2
%e A186089 ..4..3..4..0....2..2..4..4....2..4..4..0....3..4..2..3....4..2..4..0
%K A186089 nonn
%O A186089 1,1
%A A186089 _R. H. Hardin_ Feb 12 2011