[seqfan] Nice variant on a variant of A030067

[Eric Angelini]

Hello SeqFans,

Another nice seq based on the ideas here (thank you Neil!):
http://www.research.att.com/~njas/sequences/A109671

S=1,1,0,1,1,0,-1,1,2,1,-1,0,1,-1,-2,1,3,2,-1,1,2,-1,-3,0,3,1,-2,-1,1,-2,-3,1,4,3,-1,2,3,-1,-4,1,5,2,-3,-1,2,-3,-5,0,5,3,-2,1,3,-2,-5,-1,4,1,-3,-2,1,-3,-4,1,5,4,-1,3,4,-1,-5,2,7,3,-4,...

S is self-describing: "The succession of the sums of odd rank terms is the sequence itself".

In other words: underline all terms of even rank in S; these rebuild S itself; an underlined term is the sum of its two immediate neighbours.

It seems that sooner or later the sequence will show every integer, positive or negative.

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Best,
É.