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

1, 8, 41, 142, 377, 836, 1633, 2906, 4817, 7552, 11321, 16358, 22921, 31292, 41777, 54706, 70433, 89336, 111817, 138302, 169241, 205108, 246401, 293642, 347377, 408176, 476633, 553366, 639017, 734252, 839761, 956258, 1084481, 1225192, 1379177, 1547246, 1730233, 1928996, 2144417, 2377402

Offset: 1

Author

Emeric Deutsch, May 09 2018

Keywords

• nonn
• easy

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
• Emeric Deutsch and Sandi Klavžar, 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

Crossrefs

Cf. A000583, A143943.

Programs

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

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)

a(n) = A000583(n) - A143943(n-1), assuming that A143943(0) = 0. - Omar E. Pol, May 09 2018