A372976 Number of minimum edge covers in the n-double cone graph.

0, 3, 20, 27, 64, 75, 132, 147, 224, 243, 340, 363, 480, 507, 644, 675, 832, 867, 1044, 1083, 1280, 1323, 1540, 1587, 1824, 1875, 2132, 2187, 2464, 2523, 2820, 2883, 3200, 3267, 3604, 3675, 4032, 4107, 4484, 4563, 4960, 5043, 5460, 5547, 5984, 6075, 6532, 6627, 7104

Offset: 0

Author

Eric W. Weisstein, May 26 2024

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Double Cone Graph.
• Eric Weisstein's World of Mathematics, Minimum Edge Cover.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A364741.

Programs

Mathematica

a[n_] := If[Mod[n, 2] == 0, 3*n^2 + 4*n, 3*n^2]; Table[a[n], {n, 3, 44}] (* Detlef Meya, Jun 20 2024 *)
Table[n (2 + 2 (-1)^n + 3 n), {n, 0, 20}] (* Eric W. Weisstein, Dec 09 2024 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {3, 20, 27, 64, 75}, {0, 20}] (* Eric W. Weisstein, Dec 09 2024 *)
CoefficientList[Series[(x (-3 - 17 x - x^2 - 3 x^3))/((-1 + x)^3 (1 + x)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 09 2024 *)

Formula

a(n) = 3*n^2 + 4*n if (n mod 2 = 0), otherwise 3*n^2. - Detlef Meya, Jun 20 2024

From Eric W. Weisstein, Dec 09 2024: (Start)

G.f.: x*(-3-17*x-x^2-3*x^3)/((-1+x)^3*(1+x)^2).

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). (End)

Extensions

a(10) and beyond from Detlef Meya, Jun 20 2024

Offset changed to 0 and a(0)-a(2) added using the formula/recurrence by Eric W. Weisstein, Dec 09 2024