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 A362577 #17 Feb 16 2025 08:34:05
%S A362577 5,15,88,435,1957,8394,35273,146795,607492,2503687,10282873,42103670,
%T A362577 171925709,700339023,2846710048,11549292123,46778169517,189188288130,
%U A362577 764162167025,3083079787091,12426568931356,50042249662927,201366368701441,809732016511598,3254128933657397
%N A362577 Number of vertex cuts in the n-trapezohedral graph.
%C A362577 The n-trapezohedral graph is defined for n >= 3. The sequence has been extended to n=1 using the formula/recurrence. - _Andrew Howroyd_, May 03 2023
%H A362577 Andrew Howroyd, <a href="/A362577/b362577.txt">Table of n, a(n) for n = 1..500</a>
%H A362577 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrapezohedralGraph.html">Trapezohedral Graph</a>
%H A362577 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCut.html">Vertex Cut</a>
%H A362577 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (13,-65,156,-179,69,37,-38,8).
%F A362577 From _Andrew Howroyd_, May 03 2023: (Start)
%F A362577 a(n) = 3*4^n - 4*n^2 + 2*n - 2 + A005248(n) - 2*A206776(n).
%F A362577 a(n) = 13*a(n-1) - 65*a(n-2) + 156*a(n-3) - 179*a(n-4) + 69*a(n-5) + 37*a(n-6) - 38*a(n-7) + 8*a(n-8) for n > 8.
%F A362577 G.f.: x*(5 - 50*x + 218*x^2 - 514*x^3 + 577*x^4 - 160*x^5 + 28*x^6 - 8*x^7)/((1 - x)^3*(1 - 4*x)*(1 - 3*x + x^2)*(1 - 3*x - 2*x^2)).
%F A362577 (End)
%t A362577 Table[LucasL[2 n] - ((3 - Sqrt[17])^n + (3 + Sqrt[17])^n)/2^(n - 1) + 2 n - 4 n^2 + 3 4^n - 2, {n, 20}] //Expand
%t A362577 LinearRecurrence[{13, -65, 156, -179, 69, 37, -38, 8}, {5, 15, 88, 435, 1957, 8394, 35273, 146795}, 20]
%t A362577 CoefficientList[Series[(-5 + 50 x - 218 x^2 + 514 x^3 - 577 x^4 + 160 x^5 - 28 x^6 + 8 x^7)/((-1 + x)^3 (-1 + 4 x) (1 - 3 x + x^2) (-1 + 3 x + 2 x^2)), {x, 0, 20}], x]
%o A362577 (PARI) Vec((5 - 50*x + 218*x^2 - 514*x^3 + 577*x^4 - 160*x^5 + 28*x^6 - 8*x^7)/((1 - x)^3*(1 - 4*x)*(1 - 3*x + x^2)*(1 - 3*x - 2*x^2)) + O(x^30)) \\ _Andrew Howroyd_, May 03 2023
%Y A362577 Cf. A005248, A206776.
%K A362577 nonn,easy
%O A362577 1,1
%A A362577 _Eric W. Weisstein_, Apr 25 2023
%E A362577 a(1)-a(2) prepended and a(15) and beyond from _Andrew Howroyd_, May 03 2023