The generating function enumerating n by 2 0-1 matrices avoiding both vertic\
    al and horizontal patterns 010, 101 (i.e. the Mot Alone restrticion) is



                                 3      2
                              3 t  - 6 t  - 2 t - 1
                            - ---------------------
                                3      2
                               t  - 2 t  - 2 t + 1



                              and in Maple notatin



-(3*t^3-6*t^2-2*t-1)/(t^3-2*t^2-2*t+1)


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



[4, 16, 36, 100, 256, 676, 1764, 4624, 12100, 31684, 82944, 217156, 568516, 
1488400, 3896676, 10201636, 26708224, 69923044, 183060900, 479259664, 
1254718084, 3284894596, 8599965696, 22515002500, 58945041796, 154320122896, 
404015326884, 1057725857764, 2769162246400, 7249760881444, 18980120397924, 
49690600312336, 130091680539076, 340584441304900, 891661643375616, 
2334400488821956, 6111539823090244, 16000218980448784, 41889117118256100, 
109667132374319524, 287112280004702464, 751669707639787876, 1967896842914661156
, 5152020821104195600, 13488165620397925636, 35312476040089581316, 
92449262499870818304, 242035311459522873604, 633656671878697802500, 
1658934704176570533904]


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