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 A102366 #18 Oct 11 2022 18:49:44
%S A102366 1,1,2,3,6,10,15,21,28,84,120,165,220,286,364,455,1820,2380,3060,3876,
%T A102366 4845,5985,7315,8855,10626,53130,65780,80730,98280,118755,142506,
%U A102366 169911,201376,237336,278256,324632,1947792,2324784,2760681,3262623,3838380,4496388
%N A102366 Number of subsets of {1,2,...,n} in which exactly half of the elements are less than or equal to sqrt(n).
%C A102366 Also number of subsets of [n] in which exactly half of the elements are squares: a(5) = 10: {}, {1,2}, {1,3}, {1,5}, {2,4}, {3,4}, {4,5}, {1,2,3,4}, {1,2,4,5}, {1,3,4,5}. - _Alois P. Heinz_, Oct 11 2022
%H A102366 Alois P. Heinz, <a href="/A102366/b102366.txt">Table of n, a(n) for n = 0..10000</a>
%F A102366 a(n) = Sum_k C(floor(sqrt(n)),k)*C(n-floor(sqrt(n)),k) = A048093(n) + 1 = a(n-1) + A084919(n-1).
%F A102366 a(n) = binomial(n, floor(sqrt(n))). - _Paul D. Hanna_, Jun 25 2011
%e A102366 a(5) = 10 since the ten subsets of {1,2,3,4,5} are { }, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {1,2, 3,4}, {1,2, 3,5} and {1,2, 4,5}.
%o A102366 (PARI) {a(n)=if(n<0,0,binomial(n, sqrtint(n)))} /* _Paul D. Hanna_ */
%o A102366 (PARI) {a(n)=sum(k=0,sqrtint(n),binomial(sqrtint(n), k)*binomial(n-sqrtint(n),k))}
%Y A102366 Cf. A011782 for number of subsets with an even number of elements.
%Y A102366 Cf. A000290.
%K A102366 nonn
%O A102366 0,3
%A A102366 _Henry Bottomley_, Feb 22 2005