OFFSET
0,2
COMMENTS
For n >= 3, a(n) is the second Zagreb index of the graph obtained by joining one vertex of the cycle graph C[n] with each vertex of a second cycle graph C[n].
The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.
LINKS
FORMULA
G.f.: 2*x*(13-10*x)/(1-x)^3.
a(n) = 2*A370238(n). - R. J. Mathar, Apr 22 2024
Sum_{n>=1} 1/a(n) = 823467/5539688 + sqrt(3)*Pi/138-3*log(3)/46 = 0.11643041... - R. J. Mathar, Apr 22 2024
E.g.f.: exp(x)*x*(26 + 3*x). - Stefano Spezia, Apr 26 2024
EXAMPLE
a(4) = 140. Indeed, the corresponding graph has 12 edges. We list the degrees of their endpoints: (2,2), (2,2), (2,6), (2,6), (3,3), (3,3), (3,3), (3,3), (3,6), (3,6), (3,6), (3,6). Then, the second Zagreb index is 4 + 4 + 12 + 12 + 9 + 9 + 9 + 9 + 18 + 18 + 18 + 18 = 140.
MAPLE
seq(n*(3*n+23), n = 0..50);
MATHEMATICA
Table[n(3n+23), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 26, 58}, 50] (* Harvey P. Dale, Sep 30 2017 *)
PROG
(PARI) a(n)=n*(3*n+23) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 07 2016
STATUS
approved