OFFSET
0,2
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).
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
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