no trouble partiton

[koh]

    Once I calculated "boys and a girl partition", but naturally it exists on OEIS as A000070.

    I suppose if a couple exists in a partition then their parents don't like the partition because a couple may become a trouble.

    So, I considered "no trouble sequence" for parents.
    I think it is usefull for social science, but I wonder if it is interesting for Mathematics.

    %I A000001
    %S A000001 1,1,3,5,9,14,23,34

    %N A000001 Partitions of {n-1}boys and a girl with no couple.
    %e A000001    n=5
        If partitions have a pair "o*",then a(5)=12
        {o,o,o,o,*},{o,o,*,oo},{o,o,o,o*},{*,oo,oo},{o,oo,o*}, 
        {o,*,ooo},{o,o,oo*},{o*,ooo},{oo,oo*},{*,oooo},{o,ooo*},{oooo*}　
        "o" means a boy, "*" means a girl. 
        If partitions have no pair "o*",then a(5)=9
        {o,o,o,o,*},{o,o,*,oo},{*,oo,oo}, 
        {o,*,ooo},{o,o,oo*},{oo,oo*},{*,oooo},{o,ooo*},{oooo*}　

    
    %Y A000001 A000070
    %K A000001 none
    %O A000001 1,3
    %A A000001 Yasutsohi Kohmoto   zbi74583 at boat.zero.ad,jp 

    Yasutoshi