A379550 Number of minimal edge covers in the n-trapezohedral graph.

1, 9, 49, 189, 651, 2138, 6847, 21805, 69781, 225260, 734119, 2413746, 7995417, 26639534, 89150537, 299309821, 1007213417, 3394930835, 11456074815, 38688727608, 130728462411, 441894675073, 1494097644221, 5052606384210, 17088501738431, 57800015328528, 195513178028053

Offset: 1

Author

Eric W. Weisstein, Dec 25 2024

Keywords

• nonn
• easy

Comments

The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 29 2025

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Eric Weisstein's World of Mathematics, Minimal Edge Cover.
• Eric Weisstein's World of Mathematics, Trapezohedral Graph.
• Index entries for linear recurrences with constant coefficients, signature (13,-72,229,-489,797,-1075,1219,-1188,1028,-772,519,-315,158,-82,27,-13,2,-1).

Crossrefs

Cf. A356213.

Formula

G.f.: x*(1 - 4*x + 4*x^2 - 29*x^3 + 150*x^4 - 334*x^5 + 507*x^6 - 525*x^7 + 296*x^8 - 153*x^9 - 11*x^10 + 26*x^11 - 58*x^12 + 9*x^13 - 16*x^14 + 2*x^15 - x^16)/((1 - 2*x - x^3)^2*(1 - 2*x + x^2 - x^3)^3*(1 - 3*x - x^2 - x^3)). - Andrew Howroyd, May 29 2025

Extensions

a(1)-a(2) and a(8) onwards from Andrew Howroyd, May 29 2025