cp's OEIS Frontend

A304160 a(n) = n^4 - 3*n^3 + 6*n^2 - 5*n + 2 (n >= 1).

%I A304160 #30 May 28 2025 01:13:10
%S A304160 1,8,41,142,377,836,1633,2906,4817,7552,11321,16358,22921,31292,41777,
%T A304160 54706,70433,89336,111817,138302,169241,205108,246401,293642,347377,
%U A304160 408176,476633,553366,639017,734252,839761,956258,1084481,1225192,1379177,1547246,1730233,1928996,2144417,2377402
%N A304160 a(n) = n^4 - 3*n^3 + 6*n^2 - 5*n + 2 (n >= 1).
%C A304160 a(n) is the second Zagreb index of the Barbell graph B(n) (n>=3).
%C A304160 The Barbell graph B(n) is defined as two copies of the complete graph K(n) (n>=3), connected by a bridge.
%C A304160 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 A304160 The M-polynomial of the Barbell graph B(n) is M(B(n),x,y) = (n-1)*(n-2)*x^{n-1}*y^{n-1} + 2*(n-1)*x^{n-1}*y^n + x^n*y^n.
%H A304160 Colin Barker, <a href="/A304160/b304160.txt">Table of n, a(n) for n = 1..1000</a>
%H A304160 Emeric Deutsch and Sandi Klavžar, <a href="https://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 A304160 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>
%F A304160 From _Colin Barker_, May 09 2018: (Start)
%F A304160 G.f.: x*(1 + 3*x + 11*x^2 + 7*x^3 + 2*x^4) / (1 - x)^5.
%F A304160 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. (End)
%F A304160 a(n) = A000583(n) - A143943(n-1), assuming that A143943(0) = 0. - _Omar E. Pol_, May 09 2018
%o A304160 (PARI) Vec(x*(1 + 3*x + 11*x^2 + 7*x^3 + 2*x^4) / (1 - x)^5 + O(x^60)) \\ _Colin Barker_, May 09 2018
%Y A304160 Cf. A000583, A143943.
%K A304160 nonn,easy
%O A304160 1,2
%A A304160 _Emeric Deutsch_, May 09 2018