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A304160
a(n) = n^4 - 3*n^3 + 6*n^2 - 5*n + 2 (n >= 1).
2
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
1,2
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
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)
a(n) = A000583(n) - A143943(n-1), assuming that A143943(0) = 0. - Omar E. Pol, May 09 2018
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
Sequence in context: A135797 A171714 A342034 * A133106 A358588 A272843
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 09 2018
STATUS
approved