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A304832 a(n) = n^2 + 25*n - 34 (n >=2).

%I A304832 #20 May 22 2018 08:16:31
%S A304832 20,50,82,116,152,190,230,272,316,362,410,460,512,566,622,680,740,802,
%T A304832 866,932,1000,1070,1142,1216,1292,1370,1450,1532,1616,1702,1790,1880,
%U A304832 1972,2066,2162,2260,2360,2462,2566,2672,2780,2890,3002,3116,3232,3350,3470,3592,3716,3842,3970,4100,4232,4366
%N A304832 a(n) = n^2 + 25*n - 34 (n >=2).
%C A304832 a(n) is the first Zagreb index of the Mycielskian of the path graph P[n] (n > =2). For the Mycielskian, see p. 205 of the West reference and/or the Wikipedia link.
%C A304832 The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
%C A304832 For n>=3 the M-polynomial of the considered Mycielskian is 2*x^2*y^3 + 4*x^2*y^4 + 2*x^2*y^n + 2*(n-3)*x^3*y^4 + (n-2)*x^3*y^n +(n-3)*x^4*y^4.
%D A304832 D. B. West, Introduction to  Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001.
%H A304832 Colin Barker, <a href="/A304832/b304832.txt">Table of n, a(n) for n = 2..1000</a>
%H A304832 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 A304832 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mycielskian">Mycielskian</a>
%H A304832 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A304832 a(n) = A132767(n) - 34. - _Felix Fröhlich_, May 20 2018
%F A304832 From _Colin Barker_, May 21 2018: (Start)
%F A304832 G.f.: 2*x^2*(10 - 5*x - 4*x^2) / (1 - x)^3.
%F A304832 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
%F A304832 (End)
%p A304832 seq(n^2 + 25*n - 34, n = 2 .. 55);
%o A304832 (PARI) a(n) = n^2 + 25*n - 34 \\ _Felix Fröhlich_, May 20 2018
%o A304832 (PARI) Vec(2*x^2*(10 - 5*x - 4*x^2) / (1 - x)^3 + O(x^40)) \\ _Colin Barker_, May 21 2018
%o A304832 (GAP) List([2..60], n->n^2+25*n-34); # _Muniru A Asiru_, May 20 2018
%Y A304832 Cf. A132767, A304833.
%K A304832 nonn,easy
%O A304832 2,1
%A A304832 _Emeric Deutsch_, May 20 2018