This is the number of binary sequences of length n that are not 3-divided. The number that are not 2-divided turned out, surprisingly, to be A000031, so this also seems worth including.
Table of n, a(n) for n=1..29.
Cf. A210109, A000031, A209970.
Sequence in context: A066342 A340658 A291443 * A020956 A164393 A164391
Adjacent sequences: A210142 A210143 A210144 * A210146 A210147 A210148
N. J. A. Sloane, Mar 17 2012