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A158415 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 +. 1
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; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..28.

Reed Kelly and others, Discussion of this sequence

EXAMPLE

a(3)=2 because there are 2 different expressions: sqrt(sqrt(1)), 1+1.

PROG

(PARI code from Robert Gerbicz, 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]", "))

CROSSREFS

Sequence in context: A013985 A092834 A080106 * A005347 A100582 A193616

Adjacent sequences:  A158412 A158413 A158414 * A158416 A158417 A158418

KEYWORD

hard,more,nonn

AUTHOR

Vladimir Reshetnikov, Mar 18 2009

EXTENSIONS

a(19)-a(28) from Robert Gerbicz, Mar 22 2009

STATUS

approved

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Last modified September 26 06:24 EDT 2017. Contains 292502 sequences.