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A377638 Number of edge cuts in the n-gear graph.

%I A377638 #18 Jul 28 2025 02:32:41
%S A377638 1,5,45,419,3665,30795,253137,2056059,16589761,133362635,1069841265,
%T A377638 8572141979,68638314785,549385589355,4396357712337,35176668544059,
%U A377638 281439836584321,2251639520143115,18013667322023985,144111852725650139,1152906290230734305,9223302635674623915
%N A377638 Number of edge cuts in the n-gear graph.
%C A377638 The sequence has been extended to n=0 using the recurrence. - _Andrew Howroyd_, Nov 26 2024
%H A377638 Andrew Howroyd, <a href="/A377638/b377638.txt">Table of n, a(n) for n = 0..500</a>
%H A377638 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a>.
%H A377638 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>.
%H A377638 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (14,-55,58,-16).
%F A377638 G.f.: (1 - 9*x + 30*x^2 + 6*x^3)/((1 - x)*(1 - 8*x)*(1 - 5*x + 2*x^2)). - _Andrew Howroyd_, Nov 26 2024
%F A377638 a(n) = 14*a(n-1)-55*a(n-2)+58*a(n-3)-16*a(n-4). - _Eric W. Weisstein_, Dec 01 2024
%t A377638 Table[2 + 8^n - (1/2 (5 - Sqrt[17]))^n - (1/2 (5 + Sqrt[17]))^n, {n, 0, 20}] // Expand (* _Eric W. Weisstein_, Dec 01 2024 *)
%t A377638 LinearRecurrence[{14, -55, 58, -16}, {1, 5, 45, 419}, 20] (* _Eric W. Weisstein_, Dec 01 2024 *)
%t A377638 CoefficientList[Series[(1 - 9 x + 30 x^2 + 6 x^3)/((-1 + x) (-1 + 8 x) (1 - 5 x + 2 x^2)), {x, 0, 20}], x] (* _Eric W. Weisstein_, Dec 01 2024 *)
%o A377638 (PARI) Vec((1 - 9*x + 30*x^2 + 6*x^3)/((1 - x)*(1 - 8*x)*(1 - 5*x + 2*x^2)) + O(x^22)) \\ _Andrew Howroyd_, Nov 26 2024
%Y A377638 Cf. A356200, A362516.
%K A377638 nonn,easy
%O A377638 0,2
%A A377638 _Eric W. Weisstein_, Nov 03 2024
%E A377638 a(0)-a(2) prepended and a(10) onwards from _Andrew Howroyd_, Nov 26 2024