#The list below (not yet in the OEIS, Sept. 2024) consists of the first 50 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]: