OFFSET
1,2
COMMENTS
a(n) is the second Zagreb index of the Barbell graph B(n) (n>=3).
The Barbell graph B(n) is defined as two copies of the complete graph K(n) (n>=3), connected by a bridge.
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.
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.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Eric Weisstein's World of Mathematics, Independent Edge Set
FORMULA
From Colin Barker, May 09 2018: (Start)
G.f.: x*(1 + 3*x + 11*x^2 + 7*x^3 + 2*x^4) / (1 - x)^5.
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)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 09 2018
STATUS
approved