A362518 Number of vertex cuts in the n-helm graph.

1, 12, 71, 354, 1617, 7020, 29563, 122214, 499493, 2026848, 8186895, 32969754, 132508729, 531842196, 2132610467, 8545773774, 34228238925, 137046552264, 548583066679, 2195514451074, 8785586531681, 35152894560252, 140643143849931, 562667104454454, 2250951652660597

Offset

1,2

Comments

Sequence extended to n = 1 using the formula/recurrence.

Links

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

Eric Weisstein's World of Mathematics, Helm Graph

Eric Weisstein's World of Mathematics, Vertex Cut

Index entries for linear recurrences with constant coefficients, signature (13, -67, 175, -244, 172, -48).

Formula

a(n) = 2^(2*n+1) - 1 - A286184(n). - Pontus von Brömssen, Apr 23 2023

a(n) = (2^n - 1)*(1 + 2^(n + 1) - n) - 3^n.

a(n) = 13*a(n-1)-67*a(n-2)+175*a(n-3)-244*a(n-4)+172*a(n-5)-48*a(n-6).

G.f.: x*(1 - x - 18*x^2 + 60*x^3 - 84*x^4 + 48*x^5)/((-1 + x)^2*(-1 + 2*x)^2*(-1 + 3*x)*(-1 + 4*x)).

Mathematica

Table[(2^n - 1) (1 + 2^(n + 1) - n) - 3^n, {n, 20}]
LinearRecurrence[{13, -67, 175, -244, 172, -48}, {1, 12, 71, 354, 1617, 7020}, 20]
CoefficientList[Series[(1 - x - 18 x^2 + 60 x^3 - 84 x^4 + 48 x^5)/((-1 + x)^2 (-1 + 2 x)^2 (-1 + 3 x) (-1 + 4 x)), {x, 0, 20}], x]

Crossrefs

Cf. A286184.

Sequence in context: A198311 A060930 A169725 * A209447 A219302 A338261

Adjacent sequences: A362515 A362516 A362517 * A362519 A362520 A362521

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 23 2023

Extensions

More terms (based on data in A286184) from Pontus von Brömssen, Apr 23 2023

Status

approved