1,1

Every term is even: a(n) = 2*A002414(n).

a(n) is the first Zagreb index of the graph obtained by joining one vertex of a complete graph K[n] with each vertex of a second complete graph K[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph. - Emeric Deutsch, Nov 07 2016

Clark Kimberling, Table of n, a(n) for n = 1..1000

Ivan Gutman and Kinkar C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

a(n) = -n + n^2 + 2*n^3.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: f(x)/g(x), where f(x) = 2*x*(1 + 5*x) and g(x) = (1-x)^4.

From Amiram Eldar, Mar 12 2023: (Start)

Sum_{n>=1} 1/a(n) = (4*log(2) - 1)/3.

Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi - 4*log(2) + 1)/3. (End)

(See A213819.)

a[n_] := 2*n^3 + n^2 - n; Array[a, 50] (* Amiram Eldar, Mar 12 2023 *)

Cf. A002414, A213819, A328910.

Sequence in context: A114109 A085293 A119118 * A078837 A232155 A383150

Adjacent sequences: A213817 A213818 A213819 * A213821 A213822 A213823

nonn,easy

Clark Kimberling, Jul 04 2012

approved