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 A356830 #25 Feb 16 2025 08:34:03
%S A356830 0,2,12,88,520,2654,12376,54612,232788,970538,3988644,16239088,
%T A356830 65709280,264814166,1064414128,4271035692,17118683052,68563527650,
%U A356830 274481537148,1098506723080,4395504614584,17585769696206,70352578566664,281434319454084,1125797816327940
%N A356830 Number of vertex cuts in the n-prism graph.
%C A356830 Sequence extended to n = 1 using formula.
%H A356830 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H A356830 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCut.html">Vertex Cut</a>
%H A356830 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,48,-11,-22,7,4).
%F A356830 a(n) = 2^(2*n) - A286182(n) - 1. - _Pontus von Brömssen_, Aug 30 2022
%F A356830 From _Eric W. Weisstein_, Aug 31 2022: (Start)
%F A356830 a(n) = 4^n + 3*n - 3*n*Fibonacci(n, 2) - Lucas(n, 2), where Fibonacci(n, 2) = A000129(n) and Lucas(n, 2) = A002203(n).
%F A356830 a(n) = 10*a(n-1) - 35*a(n-2) + 48*a(n-3) - 11*a(n-4) - 22*a(n-5) + 7*a(n-6) + 4*a(n-7).
%F A356830 G.f.: 2*x^2*(-1 + 4*x - 19*x^2 + 18*x^3 + 10*x^4 + 6*x^5)/((-1 + x)^2*(-1 + 4*x)*(-1 + 2*x + x^2)^2). (End)
%t A356830 Table[4^n + 3 n - 3 n Fibonacci[n, 2] - LucasL[n, 2] - 2, {n, 20}]
%t A356830 LinearRecurrence[{10, -35, 48, -11, -22, 7, 4}, {0, 2, 12, 88, 520, 2654, 12376}, 20]
%t A356830 CoefficientList[Series[2 x (-1 + 4 x - 19 x^2 + 18 x^3 + 10 x^4 + 6 x^5)/((-1 + x)^2 (-1 + 4 x) (-1 + 2 x + x^2)^2), {x, 0, 20}], x]
%Y A356830 Cf. A286182, A000129, A002203.
%K A356830 nonn
%O A356830 1,2
%A A356830 _Eric W. Weisstein_, Aug 30 2022
%E A356830 More terms from _Pontus von Brömssen_, Aug 30 2022