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 A362518 #12 Feb 16 2025 08:34:05
%S A362518 1,12,71,354,1617,7020,29563,122214,499493,2026848,8186895,32969754,
%T A362518 132508729,531842196,2132610467,8545773774,34228238925,137046552264,
%U A362518 548583066679,2195514451074,8785586531681,35152894560252,140643143849931,562667104454454,2250951652660597
%N A362518 Number of vertex cuts in the n-helm graph.
%C A362518 Sequence extended to n = 1 using the formula/recurrence.
%H A362518 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HelmGraph.html">Helm Graph</a>
%H A362518 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCut.html">Vertex Cut</a>
%H A362518 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (13, -67, 175, -244, 172, -48).
%F A362518 a(n) = 2^(2*n+1) - 1 - A286184(n). - _Pontus von Brömssen_, Apr 23 2023
%F A362518 a(n) = (2^n - 1)*(1 + 2^(n + 1) - n) - 3^n.
%F A362518 a(n) = 13*a(n-1)-67*a(n-2)+175*a(n-3)-244*a(n-4)+172*a(n-5)-48*a(n-6).
%F A362518 G.f.: x*(1 - x - 18*x^2 + 60*x^3 - 84*x^4 + 48*x^5)/((-1 + x)^2*(-1 + 2*x)^2*(-1 + 3*x)*(-1 + 4*x)).
%t A362518 Table[(2^n - 1) (1 + 2^(n + 1) - n) - 3^n, {n, 20}]
%t A362518 LinearRecurrence[{13, -67, 175, -244, 172, -48}, {1, 12, 71, 354, 1617, 7020}, 20]
%t A362518 CoefficientList[Series[(1 - x - 18 x^2 + 60 x^3 - 84 x^4 + 48 x^5)/((-1 + x)^2 (-1 + 2 x)^2 (-1 + 3 x) (-1 + 4 x)), {x, 0, 20}], x]
%Y A362518 Cf. A286184.
%K A362518 nonn,easy
%O A362518 1,2
%A A362518 _Eric W. Weisstein_, Apr 23 2023
%E A362518 More terms (based on data in A286184) from _Pontus von Brömssen_, Apr 23 2023