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, 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

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) 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]", ")) \\ Robert Gerbicz, Mar 22 2009

Crossrefs

Sequence in context: A092834 A080106 A293644 * 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