A353207 Number of edge cuts in the n-helm graph.

1, 6, 54, 474, 3962, 32306, 260562, 2091746, 16758754, 134154690, 1073526594, 8589199746, 68716967810, 549747247874, 4398017264898, 35184272236034, 281474635791874, 2251798649715714, 18014394535441410, 144115174507632642, 1152921458282035202

Offset

0,2

Comments

The n-helm graph is defined for n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - Andrew Howroyd, Jan 26 2023

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Eric Weisstein's World of Mathematics, Edge Cut

Eric Weisstein's World of Mathematics, Helm Graph

Index entries for linear recurrences with constant coefficients, signature (13,-46,50,-16).

Formula

G.f.: (1 - 7*x + 22*x^2 - 2*x^3)/((1 - x)*(1 - 8*x)*(1 - 4*x + 2*x^2)). - Andrew Howroyd, Jan 26 2023

a(n) = 2 + 8^n - (2 - sqrt(2))^n - (2 + sqrt(2))^n. - Eric W. Weisstein, Mar 07 2023

Mathematica

Table[2 + 8^n - (2 - Sqrt[2])^n - (2 + Sqrt[2])^n, {n, 0, 20}] // Expand (* Eric W. Weisstein, Mar 07 2023 *)
LinearRecurrence[{13, -46, 50, -16}, {1, 6, 54, 474}, 20] (* Eric W. Weisstein, Mar 07 2023 *)
CoefficientList[Series[-((-1 + 7 x - 22 x^2 + 2 x^3)/((-1 + x) (-1 + 8 x) (1 - 4 x + 2 x^2))), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 07 2023 *)

Prog

(PARI) Vec((1 - 7*x + 22*x^2 - 2*x^3)/((1 - x)*(1 - 8*x)*(1 - 4*x + 2*x^2)) + O(x^21)) \\ Andrew Howroyd, Jan 26 2023

Crossrefs

Sequence in context: A065088 A202364 A177484 * A092810 A092472 A228413

Adjacent sequences: A353204 A353205 A353206 * A353208 A353209 A353210

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 30 2022

Extensions

a(0)-a(2) prepended and terms a(10) and beyond from Andrew Howroyd, Jan 26 2023

Status

approved