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A186090 Number of (n+2)X5 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A186090 #7 Jul 22 2025 10:14:19
%S A186090 11258613,280102672,4527262140,55707179395,558643720724,4754203179765,
%T A186090 35285910378578,232998389350277,1389861134920751,7581135805604097,
%U A186090 38188894333159149,179116588954318878,787613147423182292
%N A186090 Number of (n+2)X5 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A186090 Column 3 of A186096
%H A186090 R. H. Hardin, <a href="/A186090/b186090.txt">Table of n, a(n) for n = 1..200</a>
%F A186090 Empirical: a(n) = (73/780558954307155499190634781246950872186880000000)*n^42
%F A186090 + (13457/180824468179263822206324659748328387379200000000)*n^41
%F A186090 + (3900581/135985880541316289057601878266019315712000000000)*n^40
%F A186090 + (34573607/3547457753251729279763527259113547366400000000)*n^39
%F A186090 + (783095609/261511308733300555880003612050037145600000000)*n^38
%F A186090 + (157680394517/220220049459621520741055673305294438400000000)*n^37
%F A186090 + (4449274379387/34719377167057446963679948494077952000000000)*n^36
%F A186090 + (78266544045647/4463919921478814609615993377810022400000000)*n^35
%F A186090 + (351711904372487/185996663394950608733999724075417600000000)*n^34
%F A186090 + (6672186316510963/40397465352749453480687722876108800000000)*n^33
%F A186090 + (227175899704566161/19027791651657351277135521644544000000000)*n^32
%F A186090 + (1413399090272799163/1945063146613862574996075545886720000000)*n^31
%F A186090 + (2425160040317086077469/64234141817611026166201043229081600000000)*n^30
%F A186090 + (1308646465558482919369/772741555700583773427982474936320000000)*n^29
%F A186090 + (8213920694956950635983/124087978011418962940598943744000000000)*n^28
%F A186090 + (5617282592462587740731/2472065186946237152332244582400000000)*n^27
%F A186090 + (1521762722497945153402541/22068569627876972486051135225856000000)*n^26
%F A186090 + (1878543024001065125286721/1010003186630525056569846005760000000)*n^25
%F A186090 + (19717317282559725840243293103257/440267964076145601096720147755827200000000)*n^24
%F A186090 + (36446427572892822692407351649479/37737254063669622951147441236213760000000)*n^23
%F A186090 + (638998422910875785524665678547/34182295347526832383285725757440000000)*n^22
%F A186090 + (410339155805630961759651456959341/1262115520524067657229011412582400000000)*n^21
%F A186090 + (1597892128488008319769676720915853731/314477117197246857926228676968448000000000)*n^20
%F A186090 + (118015939736082965864789540542347989/1655142722090772936453835141939200000000)*n^19
%F A186090 + (22520321279448444798605884585883924747/25102997951710056202883166319411200000000)*n^18
%F A186090 + (208434692374593985301910711360962527/20636370256246849271643085209600000000)*n^17
%F A186090 + (40155510721702241732533453141570195711/395530429911397944373159133184000000000)*n^16
%F A186090 + (107825268730953277264995498539714242159/118659128973419383311947739955200000000)*n^15
%F A186090 + (318616883175578368540913621780089270543/44116855643963616872390826393600000000)*n^14
%F A186090 + (747073340688717248973589706042919081053/14705618547987872290796942131200000000)*n^13
%F A186090 + (443493217956706208236819899328289622001969/1407846716873544832545413136384000000000)*n^12
%F A186090 + (32621201841163616405254679822642326961/19042363199148873893680250880000000)*n^11
%F A186090 + (113921405629950674287156063055479914539627/14039603215198566480525341491200000000)*n^10
%F A186090 + (1144524508165891320553030705838759610107/34499024994611862078213980160000000)*n^9
%F A186090 + (432497307915044598355384092794497612462427/3737394374416285058473181184000000000)*n^8
%F A186090 + (61814920247335881381979777245139927327/182134228772723443395379200000000)*n^7
%F A186090 + (163824786702020604320943990364873597119237371/199243608595444170038087349903360000000)*n^6
%F A186090 + (9556363100363254083446664661866985861/5935805108544382776767462400000)*n^5
%F A186090 + (2788041811480138681735984949313139707043/1129498914940159694093465702400000)*n^4
%F A186090 + (27300487560154033333750602692383903/9743779459456174034622720000)*n^3
%F A186090 + (15469108906282154365785469517369/7285083194795024114496000)*n^2
%F A186090 + (5578947488502101228747/6258862563988320)*n
%F A186090 + 42948
%e A186090 Some solutions for 4X5
%e A186090 ..0..0..0..0..0....0..0..0..1..2....0..0..0..1..1....0..0..0..1..2
%e A186090 ..0..0..0..1..4....0..0..0..1..3....0..0..0..2..4....0..0..0..1..3
%e A186090 ..0..0..0..4..3....0..0..0..1..4....0..0..0..4..0....0..0..0..3..3
%e A186090 ..0..0..0..4..3....0..0..0..4..2....0..0..2..0..2....0..0..2..1..2
%K A186090 nonn
%O A186090 1,1
%A A186090 _R. H. Hardin_ Feb 12 2011