%I
%S 3,6,8,12,14,17,22,24,27,31,37,39,42,46,51,58,60,63,67,72,78,86,88,91,
%T 95,100,106,113,122,124,127,131,136,142,149,157,167,169,172,176,181,
%U 187,194,202,211,222,224,227,231,236,242,249,257,266,276,288,290,293,297
%N Numbers n that have a component C(1,1) when expanded in the binomial basis of order t=3.
%C Each positive integer n has a unique binomial expansion n = C(n_t,t) + C(n_{t1},t1) + ... + C(n_v,v) for a given order t, where n_t > n_{t1} > ... > n_v >= v >= 1. The sequence contains those n for which v=1 and n_v=1 at t=3. The equivalent sequence for t=2 is A000124.
%e Expansions in t=3 for n=19 up to 23 are n=19=C(5,3)+C(4,2)+C(3,1);
%e n=20=C(6,3); n=21=C(6,3)+C(2,2); n=22=C(6,3)+C(2,2)+C(1,1); n=23=C(6,3)+C(3,2).
%e Of these, only n=22 has a C(1,1) component and makes it into the sequence.
%Y Cf. A123578.
%K easy,nonn
%O 1,1
%A _R. J. Mathar_, Mar 15 2007
