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 A377771 #13 Sep 06 2025 07:05:58
%S A377771 1,13,185,3013,51009,864453,14514449,241137749,3969473217,64867543333,
%T A377771 1054153461745,17059836799733,275240835803937,4430702562116805,
%U A377771 71206049773837905,1142980976834497173,18330756374528899457,293794963549100393573,4706588394482611291313,75373885078381735479861
%N A377771 Number of edge cuts in the n-trapezohedral graph.
%C A377771 The sequence has been extended to n = 0 using the recurrence. - _Andrew Howroyd_, Dec 19 2024
%H A377771 Andrew Howroyd, <a href="/A377771/b377771.txt">Table of n, a(n) for n = 0..200</a>
%H A377771 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a>.
%H A377771 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrapezohedralGraph.html">Trapezohedral Graph</a>.
%H A377771 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (39,-531,2997,-6588,5956,-2128,256).
%F A377771 G.f.: (1 - 26*x + 209*x^2 - 296*x^3 - 636*x^4 + 248*x^5 + 80*x^6)/((1 - x)*(1 - 16*x)*(1 - 12*x + 4*x^2)*(1 - 10*x + 17*x^2 - 4*x^3)). - _Andrew Howroyd_, Dec 19 2024
%F A377771 a(n) = 39*a(n-1)-531*a(n-2)+2997*a(n-3)-6588*a(n-4)+5956*a(n-5)-2128*a(n-6)+256*a(n-7). - _Eric W. Weisstein_, Sep 06 2025
%t A377771 Table[16^n - 1 - 2^(n + 1) ChebyshevT[n, 3] + RootSum[-4 + 17 # - 10 #^2 + #^3 &, #^n &], {n, 0, 20}] (* _Eric W. Weisstein_, Sep 06 2025 *)
%t A377771 LinearRecurrence[{39, -531, 2997, -6588, 5956, -2128, 256}, {3013, 51009, 864453, 14514449, 241137749, 3969473217, 64867543333}, {-2, 20}] (* _Eric W. Weisstein_, Sep 06 2025 *)
%t A377771 CoefficientList[Series[-(1 - 26 x + 209 x^2 - 296 x^3 - 636 x^4 + 248 x^5 + 80 x^6)/((-1 + x) (-1 + 16 x) (1 - 12 x + 4 x^2) (-1 + 10 x - 17 x^2 + 4 x^3)), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 06 2025 *)
%o A377771 (PARI) Vec((1 - 26*x + 209*x^2 - 296*x^3 - 636*x^4 + 248*x^5 + 80*x^6)/((1 - x)*(1 - 16*x)*(1 - 12*x + 4*x^2)*(1 - 10*x + 17*x^2 - 4*x^3)) + O(x^21)) \\ _Andrew Howroyd_, Dec 19 2024
%Y A377771 Cf. A356213.
%K A377771 nonn,easy,changed
%O A377771 0,2
%A A377771 _Eric W. Weisstein_, Nov 06 2024
%E A377771 a(0)-a(2) prepended and a(7) onwards from _Andrew Howroyd_, Dec 19 2024