The generating function enumerating n by, 3, 0-1 matrices avoiding both verti\
    cal and horizontal patterns 010, 101 (i.e. the Mot Alone restrticion) is



                                 4       2
                              5 t  - 19 t  - 4 t - 1
                            - ----------------------
                                4      2
                               t  - 5 t  - 2 t + 1



                              and in Maple notatin



-(5*t^4-19*t^2-4*t-1)/(t^4-5*t^2-2*t+1)


            For the sake of the OEIS here are the first, 50, terms



[6, 36, 102, 378, 1260, 4374, 14946, 51384, 176238, 605022, 2076288, 7126302, 
24457806, 83942100, 288096942, 988778082, 3393583068, 11647114446, 39974047290,
137194888728, 470866430838, 1616060190870, 5546478488640, 19036063042902, 
65333652098166, 224231559219972, 769584900442134, 2641291533941226, 
9065173917994956, 31112573946476070, 106781432582484786, 366484443363408696, 
1257810875721246366, 4316931394313060142, 14816135734649867328, 
50850443997501626670, 174523755792531343614, 598982800178257760436, 
2055768243584522371614, 7055600044062831918738, 24215517550255744351932, 
83110052520647390537118, 285241924548988980462282, 978978511657152081691416, 
3359951128508993321342310, 11531684762783099660604582, 
39577883243562176947458432, 135835211789382700116248358, 
466199888668067291648446566, 1600044151520264984217530340]


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