A362516 Number of vertex cuts in the n-gear graph.

1, 5, 51, 293, 1383, 6017, 25315, 104941, 431775, 1768377, 7218555, 29388325, 119381239, 484031537, 1959295251, 7919693789, 31972642767, 128937189161, 519476334379, 2091181293589, 8412008183079, 33816433653921, 135865503379395, 545598121631437, 2190000348372223

Offset

1,2

Comments

Extended to n = 1 using formula/recurrence.

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Gear Graph

Eric Weisstein's World of Mathematics, Vertex Cut

Index entries for linear recurrences with constant coefficients, signature (10,-34,44,-13,-14,8).

Formula

a(n) = 2^(2*n+1) - 1 - A286188(n). - Pontus von Brömssen, Apr 23 2023

a(n) = 2*(4^n - 1) + 2*n - 4*n^2 - (3 - sqrt(17))/2)^n - (3 + sqrt(17))/2)^n.

a(n) = 10*a(n-1)-34*a(n-2)+44*a(n-3)-13*a(n-4)-14*a(n-5)+8*a(n-6).

G.f.: x*(-1 + 5*x - 35*x^2 + 91*x^3 + 20*x^4 + 16*x^5)/((-1 + x)^3*(1 - 7*x + 10*x^2 + 8*x^3)).

a(n) = -A206776(n)+2*4^n-2-4*n^2+2*n. - R. J. Mathar, Feb 18 2024

Mathematica

Table[2 (4^n - 1) + 2 n - 4 n^2 - (1/2 (3 - Sqrt[17]))^n - (1/2 (3 + Sqrt[17]))^n, {n, 20}] // Expand
LinearRecurrence[{10, -34, 44, -13, -14, 8}, {1, 5, 51, 293, 1383, 6017}, 20]
CoefficientList[Series[(-1 + 5 x - 35 x^2 + 91 x^3 + 20 x^4 + 16 x^5)/((-1 + x)^3 (1 - 7 x + 10 x^2 + 8 x^3)), {x, 0, 20}], x]

Crossrefs

Cf. A286188.

Sequence in context: A068540 A208997 A041043 * A369295 A145641 A317782

Adjacent sequences: A362513 A362514 A362515 * A362517 A362518 A362519

Keyword

nonn,easy,changed

Author

Eric W. Weisstein, Apr 23 2023

Extensions

More terms (based on data in A286188) from Pontus von Brömssen, Apr 23 2023

Status

approved