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%I #11 Feb 04 2018 03:16:55
%S 1,1,2,3,5,8,13,20,33,54,91,154,264,455,791,1379,2424,4277,7588,13513,
%T 24162,43336,77978,140683,254487,461409,838433,1526536
%N Number of different (by numeric value, not by structure) expressions, consisting of N symbols, each of them is one of: nullary 1, unary sqrt(), binary +.
%H Reed Kelly and others, <a href="/A158415/a158415.txt">Discussion of this sequence</a>
%e a(3)=2 because there are 2 different expressions: sqrt(sqrt(1)), 1+1.
%o (PARI) allocatemem(2*10^8);\
%o a=L=vector(28);eps=10^(-20);a[1]=[1];L[1]=1;print1(1",");\
%o for(i=2,28,b=vector(L[i-1]+sum(j=1,(i-1)\2,L[j]*L[i-j-1]));\
%o up=0;for(j=1,L[i-1],up++;b[up]=sqrt(a[i-1][j]));\
%o for(j=1,(i-1)\2,for(k=1,L[j],for(l=1,L[i-1-j],\
%o up++;b[up]=a[j][k]+a[i-1-j][l])));\
%o c=vector(up,j,b[j]);c=vecsort(c);s=0;\
%o for(j=1,up,if((j==1)||(c[j]>c[j-1]+eps),s++));\
%o a[i]=vector(s);s=0;\
%o for(j=1,up,if((j==1)||(c[j]>c[j-1]+eps),s++;a[i][s]=c[j]));\
%o L[i]=s;print1(L[i]",")) \\ _Robert Gerbicz_, Mar 22 2009
%K hard,more,nonn
%O 1,3
%A _Vladimir Reshetnikov_, Mar 18 2009
%E a(19)-a(28) from _Robert Gerbicz_, Mar 22 2009
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