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Search: id:A158415
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| A158415 |
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Number of different (by numeric value, not by structure) expressions, consisting of N symbols, each of them is one of: nullary 1, unary srqt(), binary +. |
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+0
1
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| 1, 1, 2, 3, 5, 8, 13, 20, 33, 54, 91, 154, 264, 455, 791, 1379, 2424, 4277, 7588, 13513, 24162, 43336, 77978, 140683, 254487, 461409, 838433, 1526536
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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Reed Kelly and others, Discussion of this sequence
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EXAMPLE
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a(3)=2 because there are 2 different expressions: sqrt(sqrt(1)), 1+1.
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PROGRAM
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(PARI code from Robert Gerbicz (robert.gerbicz(AT)gmail.com), Mar 22 2009)
allocatemem(2*10^8); \
a=L=vector(28); eps=10^(-20); a[1]=[1]; L[1]=1; print1(1", "); \
for(i=2, 28, b=vector(L[i-1]+sum(j=1, (i-1)\2, L[j]*L[i-j-1])); \
up=0; for(j=1, L[i-1], up++; b[up]=sqrt(a[i-1][j])); \
for(j=1, (i-1)\2, for(k=1, L[j], for(l=1, L[i-1-j], \
up++; b[up]=a[j][k]+a[i-1-j][l]))); \
c=vector(up, j, b[j]); c=vecsort(c); s=0; \
for(j=1, up, if((j==1)||(c[j]>c[j-1]+eps), s++)); \
a[i]=vector(s); s=0; \
for(j=1, up, if((j==1)||(c[j]>c[j-1]+eps), s++; a[i][s]=c[j])); \
L[i]=s; print1(L[i]", "))
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CROSSREFS
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Sequence in context: A013985 A092834 A080106 this_sequence A005347 A100582 A093093
Adjacent sequences: A158412 A158413 A158414 this_sequence A158416 A158417 A158418
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KEYWORD
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hard,more,nonn
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AUTHOR
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Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Mar 18 2009
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EXTENSIONS
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a(19)-a(28) from Robert Gerbicz (robert.gerbicz(AT)gmail.com), Mar 22 2009
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