a(3)=3 because there exist 3 different non-Brauer shortest addition chains for n=A118845(3)=21: [1 2 4 5 8 13 21] and [1 2 4 5 8 16 21] with 8=4+4 (5 not part of sum), [1 2 4 8 9 12 21] with 12=8+4 (9 not part of sum).

CROSSREFS

Cf. A118845 [numbers with shortest non-Brauer chains], A079301 [Number of minimal Brauer chains for n], A079302 [Number of minimal non-Brauer chains for n], A118844 [numbers without shortest non-Brauer chains].