1,1

(1) It appears that {a(n+1)-2a(n)} is eventually periodic, with values {1,-2,-2,-5,-5,10,-5,-5,10,-5,-5,10,-5,...}.

(2) See A139217 for the corresponding sequence using integers of the form 3k+1.

(3) Maximilian Hasler, in a SeqFan memo dated Apr. 9, 2008, notes that the Jacobsthal sequence (A001045) from a(2) on (i.e., 1,3,5,11,21,...) gives the smallest positive odd integer such that all subsets of {a(2),...,a(n)} have a different sum.

It appears that a(n)=a(n-1)+a(n-2)+2a(n-3), for n>6.

Cf. A001045, A139217.

Sequence in context: A000094 A058578 A023674 this_sequence A017988 A103077 A090980

Adjacent sequences: A139215 A139216 A139217 this_sequence A139219 A139220 A139221

nonn

John W. Layman (layman(AT)math.vt.edu), Apr 11 2008