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 A362516 #21 Mar 27 2025 02:23:40
%S A362516 1,5,51,293,1383,6017,25315,104941,431775,1768377,7218555,29388325,
%T A362516 119381239,484031537,1959295251,7919693789,31972642767,128937189161,
%U A362516 519476334379,2091181293589,8412008183079,33816433653921,135865503379395,545598121631437,2190000348372223
%N A362516 Number of vertex cuts in the n-gear graph.
%C A362516 Extended to n = 1 using formula/recurrence.
%H A362516 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>
%H A362516 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCut.html">Vertex Cut</a>
%H A362516 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-34,44,-13,-14,8).
%F A362516 a(n) = 2^(2*n+1) - 1 - A286188(n). - _Pontus von Brömssen_, Apr 23 2023
%F A362516 a(n) = 2*(4^n - 1) + 2*n - 4*n^2 - ((3 - sqrt(17))/2)^n - ((3 + sqrt(17))/2)^n.
%F A362516 a(n) = 10*a(n-1)-34*a(n-2)+44*a(n-3)-13*a(n-4)-14*a(n-5)+8*a(n-6).
%F A362516 G.f.: x*(-1 + 5*x - 35*x^2 + 91*x^3 + 20*x^4 + 16*x^5)/((-1 + x)^3*(1 - 7*x + 10*x^2 + 8*x^3)).
%F A362516 a(n) = -A206776(n)+2*4^n-2-4*n^2+2*n. - _R. J. Mathar_, Feb 18 2024
%t A362516 Table[2 (4^n - 1) + 2 n - 4 n^2 - (1/2 (3 - Sqrt[17]))^n - (1/2 (3 + Sqrt[17]))^n, {n, 20}] // Expand
%t A362516 LinearRecurrence[{10, -34, 44, -13, -14, 8}, {1, 5, 51, 293, 1383, 6017}, 20]
%t A362516 CoefficientList[Series[(-1 + 5 x - 35 x^2 + 91 x^3 + 20 x^4 + 16 x^5)/((-1 + x)^3 (1 - 7 x + 10 x^2 + 8 x^3)), {x, 0, 20}], x]
%Y A362516 Cf. A286188.
%K A362516 nonn,easy
%O A362516 1,2
%A A362516 _Eric W. Weisstein_, Apr 23 2023
%E A362516 More terms (based on data in A286188) from _Pontus von Brömssen_, Apr 23 2023