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#TI-BASIC, (削除) 106 (削除ここまで) 94 bytes

Prompt N,B
"∟B(1+remainder(n,dim(∟B→u
{1
For(I,1,N
Disp Ans
augment({0},Ans)+augment(Ans,{0
seq(Ans(X) and 2-Ans(X)+u(n-(Ans(X)<2)+dim(∟B)),X,1,dim(Ans
End

This program uses a special property of the equation variable u: when u is called with an argument, the variable n is set to one greater than that argument. For list indexing to work properly, n must be its default value of 0, and nMin should be its default 1, so either clear your calculator's RAM or set those values manually before running this.

Test case:

N=?7
B=?{0,1,0
 {1}
 {1 1}
 {1 0 1}
 {1 1 1 1}
 {1 1 0 0 1}
 {1 1 1 0 1 1}
 {1 0 0 1 1 1 1}
 Done