A356213 Number of edge covers in the n-trapezohedral graph.

4, 104, 1699, 23904, 317044, 4101107, 52473796, 668177568, 8490113467, 107776172264, 1367566963756, 17349734444643, 220090218116188, 2791852592070632, 35414167120396459, 449219270600324928, 5698208011194600148, 72279907017666274643, 916846410588661477204

Offset: 1

Author

Eric W. Weisstein, Jul 29 2022

Keywords

• nonn

Comments

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

Links

• Christian Sievers, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Edge Cover
• Eric Weisstein's World of Mathematics, Trapezohedral Graph
• Index entries for linear recurrences with constant coefficients, signature (22,-142,321,-242,74,-8).

Crossrefs

Cf. A297047.

Programs

Mathematica

Table[LucasL[2 n] - 2 ((3 - Sqrt[7])^n + (3 + Sqrt[7])^n) + ((13 - 3 Sqrt[17])^n + (13 + 3 Sqrt[17])^n)/2^n, {n, 20}] // Expand (* Eric W. Weisstein, May 26 2024 *)
LinearRecurrence[{22, -142, 321, -242, 74, -8}, {4, 104, 1699, 23904, 317044, 4101107}, 20] (* Eric W. Weisstein, May 26 2024 *)
CoefficientList[Series[-(((-2 + x) (2 + 9 x - 6 x^2 + 2 x^3))/((1 - 3 x + x^2) (1 - 6 x + 2 x^2) (1 - 13 x + 4 x^2))), {x, 0, 20}], x] (* Eric W. Weisstein, May 26 2024 *)

Formula

a(n) = 22*a(n-1) - 142*a(n-2) + 321*a(n-3) - 242*a(n-4) + 74*a(n-5) - 8*a(n-6) for n > 6.

G.f.: -(-2+x)*x*(2+9*x-6*x^2+2*x^3)/((1-3*x+x^2)*(1-6*x+2*x^2)*(1-13*x+4*x^2)).

Extensions

a(9)-a(12) from Andrew Howroyd, Jan 27 2023

More terms from Christian Sievers, Nov 20 2023

a(1)-a(2) prepended by Eric W. Weisstein, May 26 2024

Offset updated for a(1)-a(2) by Sean A. Irvine, Aug 11 2024