longd1_function(ps,pss,pff,n,d)
{
#this program compute the probability P(N(n,d)=0)#
#i.e., the number of non-overlapping type 1 runs having at most 1 type 0 # 
#under given initial ps and pf with length d is zero.d=#1+#0#
NN_((1+d)*d/2)+1
pf_1-ps
psf_1-pss
pfs_1-pff 
c0_matrix(0,1,NN-1)
p0_cbind(1,c0)
c1_matrix(1,NN-1,1)
U_rbind(c1,0)
M_matrix(0,NN,NN)
 for(ir in 0:(d-1)) {
   for(jr in 0:ir){ 
     for(ic in 0:(d-1)) {
       for(jc in 0:ic){
          rid_((ir+1)*ir/2)+jr+1
          cid_((ic+1)*ic/2)+jc+1
          if( ir>0 && jr==0 && ic==ir+1 && jc==0){M[rid,cid]_pss}
          if(jr>1 && ic==ir+1 && jc==jr+1){M[rid,cid]_pss}
          if(ir>0 && ic==ir+1 && jr==0 && jc==1){M[rid,cid]_psf}
          if(jr>0 && ic==jr && jc==1){M[rid,cid]_psf}
          if(ir>0 && jr==1 && ic==1 && jc==1){M[rid,cid]_pff}
          if(ir>0 && jr==1 && ic==ir+1 && jc==2){M[rid,cid]_pfs}
          if(ir==0 && jr==0 && ic==1 && jc==0){M[rid,cid]_ps}
          if(ir==0 && jr==0 && ic==1 && jc==1){M[rid,cid]_pf}
}}}}
for(i in 1:NN) { M[i,NN]_1-sum(M[i,]) }
Mn_M%*%M
for (i in 3:n) {Mn_Mn%*%M }
1-p0%*%Mn%*%U
}