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

1, 2, 6, 26, 122, 562, 2514, 10978, 47074, 199106, 833346, 3459458, 14268290, 58542850, 239189250, 973889026, 3954048514, 16015899650, 64745436162, 261309683714, 1053186816002, 4239883710466, 17052184465410, 68525063462914, 275180257009666, 1104408389468162

Offset: 1

Author

Eric W. Weisstein, Oct 30 2024

Keywords

• nonn
• easy

Comments

a(n) is also the number of edge cuts in the wheel graph on n vertices for n > 3.

Links

• Eric Weisstein's World of Mathematics, Edge Cut.
• Eric Weisstein's World of Mathematics, Wheel Graph.
• Index entries for linear recurrences with constant coefficients, signature (9,-26,26,-8).

Crossrefs

Cf. A158525.

Programs

Mathematica

Table[2 + 4^(n - 1) - (2 - Sqrt[2])^(n - 1) - (2 + Sqrt[2])^(n - 1), {n, 26}]
LinearRecurrence[{9, -26, 26, -8}, {1, 2, 6, 26}, 20]
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]

Formula

a(n) = 2 + 4^(n - 1) - (2 - sqrt(2))^(n - 1) - (2 + sqrt(2))^(n - 1) = 2+4^(n-1)-2*A006012(n-1).

a(n) = 9*a(n-1)-26*a(n-2)+26*a(n-3)-8*a(n-4).

G.f.: -x*(-1+7*x-14*x^2+2*x^3)/((-1+x)*(-1+4*x)*(1-4*x+2*x^2)).

a(n) = 2^(2*(n-1))-A158525(n) for n >= 4. - Pontus von Brömssen, Nov 06 2024

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