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A351992
Number of minimum edge covers in the n-vertex wheel graph.
0
0, 1, 4, 3, 14, 5, 30, 7, 52, 9, 80, 11, 114, 13, 154, 15, 200, 17, 252, 19, 310, 21, 374, 23, 444, 25, 520, 27, 602, 29, 690, 31, 784, 33, 884, 35, 990, 37, 1102, 39, 1220, 41, 1344, 43, 1474, 45, 1610, 47, 1752, 49, 1900, 51, 2054, 53, 2214, 55, 2380, 57, 2552, 59, 2730
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
Eric Weisstein's World of Mathematics, Minimum Edge Cover
Eric Weisstein's World of Mathematics, Wheel Graph
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, 20}]
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 5, 3, 16, 5}, 20]
Table[(3 n^2 + 2 n - 3 (-1)^n (n - 1)^2 - 5)/8, {n, 20}]
CoefficientList[Series[x (-1 - 5 x - x^3 + x^4)/(-1 + x^2)^3, {x, 0, 20}], x]
CROSSREFS
Sequence in context: A019136 A298057 A140884 * A082383 A216486 A321262
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Feb 27 2022
STATUS
approved