cp's OEIS Frontend

A304839 a(n) = 61*n - 38 (n>=1).

%I A304839 #13 Jan 05 2025 19:51:41
%S A304839 23,84,145,206,267,328,389,450,511,572,633,694,755,816,877,938,999,
%T A304839 1060,1121,1182,1243,1304,1365,1426,1487,1548,1609,1670,1731,1792,
%U A304839 1853,1914,1975,2036,2097,2158,2219,2280,2341,2402,2463,2524,2585,2646,2707,2768,2829,2890,2951,3012
%N A304839 a(n) = 61*n - 38 (n>=1).
%C A304839 For n>=2, a(n) is the  second Zagreb index of the angular phenylene shown in the Bodroza-Pantic et al. reference (Fig. 1 (b)).
%C A304839 The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
%C A304839 The M-polynomial of the angular phenylene A(n) is M(A(n); x, y) = (n + 4)*x^2*y^2 + 2*n*x^2*y^3 + (5*n - 6)*x^3*y^3.
%H A304839 Colin Barker, <a href="/A304839/b304839.txt">Table of n, a(n) for n = 1..1000</a>
%H A304839 O. Bodroza-Pantic, I. Gutman, and S. J. Cyvin, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/35-1/bodroza-pantic.pdf">Fibonacci numbers and algebraic structure count of some non-benzenoid conjugated polymers</a>, The Fibonacci Quarterly, 35, 1, 1997, 75-83.
%H A304839 E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H A304839 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A304839 From _Colin Barker_, May 24 2018: (Start)
%F A304839 G.f.: x*(23 + 38*x) / (1 - x)^2.
%F A304839 a(n) = 2*a(n-1) - a(n-2) for n>2.
%F A304839 (End)
%p A304839 seq(61*n-38, n = 1 .. 50);
%t A304839 Array[61#-38&,50] (* _Harvey P. Dale_, Nov 23 2022 *)
%o A304839 (PARI) Vec(x*(23 + 38*x) / (1 - x)^2 + O(x^40)) \\ _Colin Barker_, May 24 2018
%Y A304839 Cf. A304157.
%K A304839 nonn,easy
%O A304839 1,1
%A A304839 _Emeric Deutsch_, May 24 2018