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 A120739 #23 Sep 08 2022 08:45:26
%S A120739 0,0,1,2,7,14,30,60,127,254,510,1020,2046,4092,8188,16376,32767,65534,
%T A120739 131070,262140,524286,1048572,2097148,4194296,8388606,16777212,
%U A120739 33554428,67108856,134217724,268435448,536870904,1073741808,2147483647
%N A120739 a(n) = Sum_{k=0..n} floor(C(n,k)/2).
%C A120739 Nonzero terms = row sums of triangle A166454. - _Gary W. Adamson_, Oct 14 2009
%H A120739 Charles R Greathouse IV, <a href="/A120739/b120739.txt">Table of n, a(n) for n = 0..3322</a>
%H A120739 Pantelimon Stanica, Tsutomu Sasao, Jon T. Butler, <a href="http://faculty.nps.edu/butler/PDF/2017/Stanica_Sasao_Butler_JCMCC.pdf">Distance Duality on Some Classes of Boolean Functions</a>, Journal of Combinatorial Mathematics and Combinatorial Computing (to appear), 2017. [Theorem 9.]
%F A120739 a(n) = (2^n - A001316(n))/2.
%t A120739 Table[Sum[Floor[Binomial[n,k]/2], {k,0,n}], {n,0,40}] (* _G. C. Greubel_, Apr 18 2019 *)
%o A120739 (PARI) a(n)=(2^n-2^norml2(binary(n)))/2
%o A120739 (PARI) {a(n) = sum(k=0,n, binomial(n,k)\2)}; \\ _G. C. Greubel_, Apr 18 2019
%o A120739 (Haskell)
%o A120739 a120739 n = if n < 2 then 0 else sum $ a166454_row n
%o A120739 -- _Reinhard Zumkeller_, Mar 04 2015
%o A120739 (Magma) [(&+[Floor(Binomial(n,k)/2): k in [0..n]]): n in [0..40]]; // _G. C. Greubel_, Apr 18 2019
%o A120739 (Sage) [sum(floor(binomial(n,k)/2) for k in (0..n)) for n in (0..40)] # _G. C. Greubel_, Apr 18 2019
%Y A120739 Cf. A001316, A011848, A166454.
%K A120739 easy,nonn
%O A120739 0,4
%A A120739 _Paul Barry_, Jun 29 2006