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A377501 a(n) = 2 + 4^(n - 1) - (2 - sqrt(2))^(n - 1) - (2 + sqrt(2))^(n - 1).

%I A377501 #14 Dec 15 2024 09:06:28
%S A377501 1,2,6,26,122,562,2514,10978,47074,199106,833346,3459458,14268290,
%T A377501 58542850,239189250,973889026,3954048514,16015899650,64745436162,
%U A377501 261309683714,1053186816002,4239883710466,17052184465410,68525063462914,275180257009666,1104408389468162
%N A377501 a(n) = 2 + 4^(n - 1) - (2 - sqrt(2))^(n - 1) - (2 + sqrt(2))^(n - 1).
%C A377501 a(n) is also the number of edge cuts in the wheel graph on n vertices for n > 3.
%H A377501 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a>.
%H A377501 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>.
%H A377501 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,26,-8).
%F A377501 a(n) = 2 + 4^(n - 1) - (2 - sqrt(2))^(n - 1) - (2 + sqrt(2))^(n - 1) = 2+4^(n-1)-2*A006012(n-1).
%F A377501 a(n) = 9*a(n-1)-26*a(n-2)+26*a(n-3)-8*a(n-4).
%F A377501 G.f.: -x*(-1+7*x-14*x^2+2*x^3)/((-1+x)*(-1+4*x)*(1-4*x+2*x^2)).
%F A377501 a(n) = 2^(2*(n-1))-A158525(n) for n >= 4. - _Pontus von Brömssen_, Nov 06 2024
%F A377501 E.g.f.: exp(2*x)*(-2*cosh(sqrt(2)*x) - 2*sinh(x) + cosh(x)*(2 + sinh(x)) + sqrt(2)*sinh(sqrt(2)*x)). - _Stefano Spezia_, Nov 08 2024
%t A377501 Table[2 + 4^(n - 1) - (2 - Sqrt[2])^(n - 1) - (2 + Sqrt[2])^(n - 1), {n, 26}]
%t A377501 LinearRecurrence[{9, -26, 26, -8}, {1, 2, 6, 26}, 20]
%t A377501 CoefficientList[Series[-(-1 + 7 x - 14 x^2 + 2 x^3)/((-1 + x) (-1 + 4 x) (1 - 4 x + 2 x^2)), {x, 0, 20}], x]
%Y A377501 Cf. A158525.
%K A377501 nonn,easy
%O A377501 1,2
%A A377501 _Eric W. Weisstein_, Oct 30 2024