This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A277976 #18 Apr 26 2024 19:27:04
%S A277976 0,26,58,96,140,190,246,308,376,450,530,616,708,806,910,1020,1136,
%T A277976 1258,1386,1520,1660,1806,1958,2116,2280,2450,2626,2808,2996,3190,
%U A277976 3390,3596,3808,4026,4250,4480,4716,4958,5206,5460,5720,5986,6258,6536
%N A277976 a(n) = n*(3*n + 23).
%C A277976 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].
%C A277976 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.
%H A277976 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A277976 G.f.: 2*x*(13-10*x)/(1-x)^3.
%F A277976 a(n) = 2*A370238(n). - _R. J. Mathar_, Apr 22 2024
%F A277976 Sum_{n>=1} 1/a(n) = 823467/5539688 + sqrt(3)*Pi/138-3*log(3)/46 = 0.11643041... - _R. J. Mathar_, Apr 22 2024
%F A277976 E.g.f.: exp(x)*x*(26 + 3*x). - _Stefano Spezia_, Apr 26 2024
%e A277976 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.
%p A277976 seq(n*(3*n+23), n = 0..50);
%t A277976 Table[n(3n+23),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,26,58},50] (* _Harvey P. Dale_, Sep 30 2017 *)
%o A277976 (PARI) a(n)=n*(3*n+23) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A277976 Cf. A132761, A370238.
%K A277976 nonn,easy
%O A277976 0,2
%A A277976 _Emeric Deutsch_, Nov 07 2016