[seqfan] possible relation in A005132 Recaman's sequence

Georgi Guninski guninski at guninski.com
Wed Jun 3 10:05:57 CEST 2009


http://www.research.att.com/~njas/sequences/?q=A005132&sort=0&fmt=0&language=english&go=Search
A005132  Recaman's sequence: a(0) = 0; for n > 0, a(n) = a(n-1)-n if
that number is positive and not already in the sequence, otherwise a(n)
= a(n-1)+n

seems to satisfy:

a(n-2)^2 - 2*a(n-2)*a(n-1) - a(n-1)^2 + 4*a(n-1)*a(n) - a(n)^2 
- 2*a(n)*a(n+1) + a(n+1)^2 - 2 = 0

( x^2 - 2*x*y - y^2 + 4*y*z - z^2 - 2*z*t + t^2 - 2 = 0 )

verified to 10^5 using the B file from OEIS.





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