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A126862 Numbers n that have a component C(1,1) when expanded in the binomial basis of order t=3. 0

%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_{t-1},t-1) + ... + C(n_v,v) for a given order t, where n_t > n_{t-1} > ... > 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

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Last modified July 12 11:04 EDT 2020. Contains 335658 sequences. (Running on oeis4.)