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 A084635 #16 Mar 22 2023 08:13:39
%S A084635 1,1,2,4,8,17,38,86,192,419,894,1872,3864,7893,16006,32298,64960,
%T A084635 130375,261310,523300,1047416,2095801,4192742,8386814,16775168,
%U A084635 33552107,67106238,134214776,268432152,536867229,1073737734,2147479122,4294962304,8589929103
%N A084635 Binomial transform of 1,0,1,0,1,1,1,...
%C A084635 Without its first term, it is the binomial transform of 1,1,1,1,2,2,2,2,2...
%H A084635 G. C. Greubel, <a href="/A084635/b084635.txt">Table of n, a(n) for n = 0..1000</a>
%H A084635 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).
%F A084635 a(n) = 2^n - n*(n^2 - 3*n + 8)/6.
%F A084635 a(n) = 1 + C(n, 2) + Sum_{k=4..n} C(n, k).
%F A084635 O.g.f.: (1-5*x+10*x^2-10*x^3+5*x^4)/((1-x)^4*(1-2*x)). - _R. J. Mathar_, Apr 02 2008
%F A084635 a(n) = A000225(n) - (n-1) - binomial(n, 3). - _G. C. Greubel_, Mar 19 2023
%t A084635 Table[2^n -n -Binomial[n,3], {n,0,50}] (* _G. C. Greubel_, Mar 19 2023 *)
%o A084635 (Magma) [2^n -n*(n^2-3*n+8)/6: n in [0..50]]; // _G. C. Greubel_, Mar 19 2023
%o A084635 (SageMath) [2^n -n*(n^2-3*n+8)/6 for n in range(51)] # _G. C. Greubel_, Mar 19 2023
%Y A084635 Cf. A000225, A000325, A084634.
%K A084635 easy,nonn
%O A084635 0,3
%A A084635 _Paul Barry_, Jun 06 2003