1,2

(1) It appears that {a(n+1)-2a(n)} is eventually periodic, with values {2,-1,-1,-4,5,-1,-4,5,-1,-4,5,-1,-4,...}.

(2) See A139218 for the corresponding sequence using integers of the form 3k+2.

(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>4.

Cf. A001045, A139218.

Adjacent sequences: A139214 A139215 A139216 this_sequence A139218 A139219 A139220

Sequence in context: A068940 A008471 A111314 this_sequence A038391 A090854 A039694

nonn

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