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

Author

Eric W. Weisstein, Apr 23 2023

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Crossrefs

Cf. A286184.

Programs

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]

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)).

Extensions

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