This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A126862 #8 Aug 06 2025 00:33:24
%S A126862 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 A126862 95,100,106,113,122,124,127,131,136,142,149,157,167,169,172,176,181,
%U A126862 187,194,202,211,222,224,227,231,236,242,249,257,266,276,288,290,293,297
%N A126862 Numbers k that have a component C(1,1) when expanded in the binomial basis of order t=3.
%C A126862 Each positive integer k has a unique binomial expansion k = C(k_t,t) + C(k_{t-1},t-1) + ... + C(k_v,v) for a given order t, where k_t > k_{t-1} > ... > k_v >= v >= 1. The sequence contains those k for which v=1 and k_v=1 at t=3. The equivalent sequence for t=2 is A000124.
%e A126862 Expansions in t=3 for k=19 up to 23 are k=19=C(5,3)+C(4,2)+C(3,1);
%e A126862 k=20=C(6,3); k=21=C(6,3)+C(2,2); k=22=C(6,3)+C(2,2)+C(1,1); k=23=C(6,3)+C(3,2).
%e A126862 Of these, only k=22 has a C(1,1) component and makes it into the sequence.
%t A126862 With[{res = Map[ResourceFunction["BinomialNumberSystemTriplet"], Range[300]]},Position[res[[All, 1]], 1] // Flatten] (* _Shenghui Yang_, Jul 31 2025 *)
%Y A126862 Cf. A123578.
%K A126862 easy,nonn
%O A126862 1,1
%A A126862 _R. J. Mathar_, Mar 15 2007