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A048493 a(n) = (n+1)*2^n - n.

%I A048493 #31 Feb 16 2025 08:32:40
%S A048493 1,3,10,29,76,187,442,1017,2296,5111,11254,24565,53236,114675,245746,
%T A048493 524273,1114096,2359279,4980718,10485741,22020076,46137323,96468970,
%U A048493 201326569,419430376,872415207,1811939302,3758096357,7784628196,16106127331,33285996514
%N A048493 a(n) = (n+1)*2^n - n.
%C A048493 Old definition was: "a(n) = T(n,n), array T given by A048483".
%C A048493 Also the number of connected induced subgraphs in the n-sunlet graph. - _Eric W. Weisstein_, May 25 2017
%H A048493 Vincenzo Librandi, <a href="/A048493/b048493.txt">Table of n, a(n) for n = 0..2000</a>
%H A048493 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SunletGraph.html">Sunlet Graph</a>
%H A048493 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>
%H A048493 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F A048493 a(n) = (n+1)*2^n-n. - _Vladeta Jovovic_, Feb 28 2003
%F A048493 a(n) = 5*a(n-1)-7*a(n-2)-a(n-3)+8*a(n-4)-4*a(n-5). - _Colin Barker_, Nov 26 2014
%F A048493 G.f.: -(4*x^3-5*x^2+3*x-1) / ((x-1)^2*(2*x-1)^2). - _Colin Barker_, Nov 26 2014
%t A048493 Table[(n + 1) 2^n - n, {n, 20}] (* _Eric W. Weisstein_, May 25 2017 *)
%t A048493 Table[2^n + (2^n - 1) n, {n, 20}] (* _Eric W. Weisstein_, May 25 2017 *)
%t A048493 LinearRecurrence[{6, -13, 12, -4}, {3, 10, 29, 76}, 20] (* _Eric W. Weisstein_, May 25 2017 *)
%o A048493 (Magma) [(n+1)*2^n-n: n in [0..30]]; // _Vincenzo Librandi_, Sep 26 2011
%o A048493 (PARI) Vec(-(4*x^3-5*x^2+3*x-1)/((x-1)^2*(2*x-1)^2) + O(x^100)) \\ _Colin Barker_, Nov 26 2014
%Y A048493 Cf. A058877.
%K A048493 nonn,easy
%O A048493 0,2
%A A048493 _Clark Kimberling_
%E A048493 Description changed to more explicit formula by _Eric W. Weisstein_, May 25 2017