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A372976
Number of minimum edge covers in the n-double cone graph.
1
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
0,2
LINKS
Eric Weisstein's World of Mathematics, Double Cone Graph.
Eric Weisstein's World of Mathematics, Minimum Edge Cover.
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)
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 *)
CROSSREFS
Cf. A364741.
Sequence in context: A022129 A308721 A053748 * A075358 A352810 A002461
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 26 2024
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
STATUS
approved