A370238 -id:A370238 - cp's OEIS frontend

0, 26, 58, 96, 140, 190, 246, 308, 376, 450, 530, 616, 708, 806, 910, 1020, 1136, 1258, 1386, 1520, 1660, 1806, 1958, 2116, 2280, 2450, 2626, 2808, 2996, 3190, 3390, 3596, 3808, 4026, 4250, 4480, 4716, 4958, 5206, 5460, 5720, 5986, 6258, 6536

Offset: 0

Emeric Deutsch, Nov 07 2016

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.

			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.

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

Cf. A132761, A370238.

Maple
```
seq(n*(3*n+23), n = 0..50);
```

Table[n(3n+23),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,26,58},50] (* Harvey P. Dale, Sep 30 2017 *)

a(n)=n*(3*n+23) \\ Charles R Greathouse IV, Jun 17 2017

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

cp's OEIS Frontend

A277976 a(n) = n(3n + 23).

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