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 A132732 #28 Feb 16 2025 08:33:06
%S A132732 1,2,4,10,24,54,116,242,496,1006,2028,4074,8168,16358,32740,65506,
%T A132732 131040,262110,524252,1048538,2097112,4194262,8388564,16777170,
%U A132732 33554384,67108814,134217676,268435402,536870856,1073741766,2147483588,4294967234,8589934528
%N A132732 Row sums of triangle A132731.
%C A132732 a(n) is the number of connected induced subgraphs in the (n+1)-path complement graph. - _Eric W. Weisstein_, Apr 11 2018
%H A132732 G. C. Greubel, <a href="/A132732/b132732.txt">Table of n, a(n) for n = 0..1000</a>
%H A132732 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H A132732 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathComplementGraph.html">Path Complement Graph</a>
%H A132732 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>
%H A132732 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A132732 Binomial transform of [1, 1, 1, 3, 1, 3, 1, 3, 1, ... (3,1 repeated)].
%F A132732 a(n) = 2*(2^n-n) = 2*A000325(n), n>0. - _R. J. Mathar_, Sep 16 2017
%F A132732 G.f.: (1 - 2*x + x^2 + 2*x^3)/((1-x)^2 * (1-2*x)). - _Eric W. Weisstein_, Apr 11 2018
%F A132732 E.g.f.: -1 - 2*x*exp(x) + 2*exp(2*x). - _G. C. Greubel_, Feb 14 2021
%e A132732 a(3) = 10 = sum of row 3 terms of triangle A132731: (1 + 4 + 4 + 1).
%e A132732 a(3) = 10 = (1, 3, 3, 1) dot (1, 1, 1, 3) = (1 + 3 + 3 + 3).
%t A132732 Join[{1}, Table[2 (2^n - n), {n, 20}]] (* or *)
%t A132732 Join[{1}, LinearRecurrence[{4, -5, 2}, {2, 4, 10}, 20]] (* or *)
%t A132732 CoefficientList[Series[(1 -2x +x^2 +2x^3)/((1-x)^2 (1-2x)), {x, 0, 20}], x] (* _Eric W. Weisstein_, Apr 11 2018 *)
%o A132732 (PARI) a(n) = if(n==0, 1, 2*(2^n -n)); \\ _Altug Alkan_, Apr 12 2018
%o A132732 (Sage) [1]+[2*(2^n -n) for n in (1..30)] # _G. C. Greubel_, Feb 14 2021
%o A132732 (Magma) [1] cat [2*(2^n -n): n in [1..30]]; // _G. C. Greubel_, Feb 14 2021
%Y A132732 Cf. A132731.
%K A132732 nonn,easy
%O A132732 0,2
%A A132732 _Gary W. Adamson_, Aug 26 2007