A351992 Number of minimum edge covers in the n-vertex wheel graph.

0, 1, 5, 3, 16, 5, 33, 7, 56, 9, 85, 11, 120, 13, 161, 15, 208, 17, 261, 19, 320, 21, 385, 23, 456, 25, 533, 27, 616, 29, 705, 31, 800, 33, 901, 35, 1008, 37, 1121, 39, 1240, 41, 1365, 43, 1496, 45, 1633, 47, 1776, 49, 1925, 51, 2080, 53, 2241, 55, 2408, 57, 2581, 59, 2760

Offset

1,3

Comments

The wheel graph is well defined on n >= 4 vertices; sequence extended to n = 1 using the formulas/generating function.

Links

Table of n, a(n) for n=1..61.

Eric Weisstein's World of Mathematics, Minimum Edge Cover.

Eric Weisstein's World of Mathematics, Wheel Graph.

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

a(n) = n - 1 for n == 0 (mod 2).

a(n) = (n - 1)*(3*n + 1)/4 for n == 1 (mod 2).

a(n) = (3*n^2 + 2*n - 3*(-1)^n*(n - 1)^2 - 5)/8.

G.f.: x^2*(-1 - 5*x - x^3 + x^4)/(-1 + x^2)^3.

E.g.f.: (4 + (x - 4)*cosh(x) + (3*x^2 + 4*x - 1)*sinh(x))/4. - Stefano Spezia, Mar 15 2022

Mathematica

Table[Piecewise[{{n - 1, Mod[n, 2] == 0}, {(n - 1) (3 n + 1)/4, Mod[n, 2] == 1}}, 0], {n, 61}]
(* Alternative: *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 5, 3, 16, 5}, 61]
(* Alternative: *)
Table[(3 n^2 + 2 n - 3 (-1)^n (n - 1)^2 - 5)/8, {n, 61}]
(* Alternative: *)
CoefficientList[Series[x (-1 - 5 x - x^3 + x^4)/(-1 + x^2)^3, {x, 0, 60}], x]

Crossrefs

Bisections are A005408 (even) and A045944 (odd).

Sequence in context: A189237 A301494 A053371 * A199005 A217415 A213571

Adjacent sequences: A351989 A351990 A351991 * A351993 A351994 A351995

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 27 2022

Extensions

Odd terms corrected by Falk Hüffner, Jun 23 2026

Status

approved