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<DIV><FONT face=Arial size=2>It seems to me that A001650 "wants" to start at
index 0 instead of index 1. </FONT><FONT face=Arial size=2>If we do this, the
formulae simplify and special cases disappear, so that the current</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>%F A001650 a(n) = 1 + 2*floor(sqrt(n-1)), n > 0.
- Antonio Esposito (antonio.b.esposito(AT)italtel.it), Jan 21 2002<BR>%F
A001650 G.f.: theta_3(x)*x/(1-x). a(n+1)=a(n)+A000122(n). - Michael Somos, Apr
29 2003.<BR>%o A001650 (PARI) a(n)=if(n<1,0,1+2*sqrtint(n-1))</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>becomes</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>%F A001650 a(n) = 1 + 2*floor(sqrt(n)). - Antonio
Esposito (antonio.b.esposito(AT)italtel.it), Jan 21 2002<BR>%F A001650
G.f.: theta_3(x)/(1-x). </FONT><FONT face=Arial size=2>a(n)=a(n-1)+A000122(n). -
Michael Somos, Apr 29 2003.<BR>%o A001650 (PARI)
a(n)=1+2*sqrtint(n)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>My interest in making this change is that it
also makes A001650 consistent with a batch of sequences I </FONT><FONT
face=Arial size=2>plan to submit in the near future.</FONT><FONT face=Arial
size=2></DIV></FONT><FONT face=Arial></FONT>
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