#The list below (not yet in the OEIS, Sept. 2024) consists of the first 70 terms of the sequence enumerating
#6 by 2n 0-1 matrices with row sums 3 and column sums n (i.e. every row and every column has as many 0s as 1s)
#and in addition satisfy the "Not Alone" condition, i.e. avoiding the patterns 010 and 101 both in rows and columns

L:=
[ 8, 64, 368, 2776, 25880, 251704, 2629080, 28964248, 331032312, 
 3907675376, 47392320240, 587548108400, 7421689479608, 95248568409312, 
 1239031994818680, 16306127772957216, 216760982171930144, 
 2906731043068293952, 39278080769921432856, 534346120254755625336, 
 7312907424570010667248, 100617168758718590691008, 1391010806098829548194904, 
 19313535594682146548460528, 269209923705508842284676904, 
 3765886492662164678445053416, 52851694610761401821852209616, 
 743962982623636240768303150120, 10501311671694580295922263260952, 
 148609448060243565827017350779120, 2108049309306125909820857999346600, 
 29969253228287252676404113071031720, 426941671703804052186698458236393640, 
 6093988211579593205052790422166943248, 
 87141204396467460974950644844239972640, 
 1248209867628787897877252927395624298032, 
 17908168513672928265660640827189828359808, 
 257321055095793668871823289163036419826432, 
 3702750088815541170579059742737023650455464, 
 53353833519948633030908875850765217961334088, 
 769783869784638430203994130666426616298686280, 
 11120031911494876529357210044442442181208901328, 
 160824229134303817300193733254803175054621520408, 
 2328526427637923157623531007418389227748523893504, 
 33749926016852785225950721365493720398282348567080, 
 489672458176311265031102196666211015094603158858176, 
 7111485884391990632560537289137700066611348614975888, 
 103375764774983064830826387520428185616465121487764328, 
 1504055515395625741293226832240893342914345948366930392, 
 21901801616028639271764709973872070744841033566502070016, 
 319191797371570116676504503232222431289020253675541027568, 
 4655490719330192862731901611013971932694605070406760485176, 
 67952876323177957548968147062216621305698484705257503288216, 
 992581990952901187419897507166015487121849528996558294681344, 
 14508727940648157727313372819875225784236953415557348717884696, 
 212219633964507319718182913983832392356267535421538529632258872, 
 3106165152510218692020067123418617685516759779453002622652515032, 
 45492135183886435428437962859407884801827363205881951578268209816, 
 666670827846406027513138826009877795264546308596187030018259654136, 
 9775544913423874267517709591092502189345226742549331946149654902312, 
 143422201036486366745270629166282823626430843842389970479355159878864, 
 2105375606659307747572547074500920119618361241175268438762309576345608, 
 30922378499090885698160750305079994315718671626570060073328421459908688, 
 454400679010016156836652921265507183483930334464637077224159999352974872, 
 6680682698302319853432938119782337945180670004562092336954438477439833496, 
 98267940658245387744135730775239929861765131726148168711579856043883369672, 
 1446124376774511644887441816558044033871868607099983649771724243881608392592, 
 21291004574451856559155591663800751263312334621002669854527643659909322637632,
 313601098021938355635698981404665678702173175469049040089232039946027459253888,
 4621089339239598121743385036836452065887756116850562092129006812168660020588728]: