[seqfan] Re: New formula for A030101 ?

David Applegate david at research.att.com
Sun Mar 16 17:33:36 CET 2014


I believe you have a typo.  From http://projecteuler.net/problem=463,
the recurrence is:
   f(1)=1
   f(3)=3
   f(2n)=f(n)
   f(4n+1)=2f(2n+1)-f(n)
   f(4n+3)=3f(2n+1)-2f(n)   ("-", not "+").

And this is indeed a recurrence for A030101, as can readily be seen
expanding the recurrence into binary strings and reversals.

-Dave




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