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A304161 a(n) = 2*n^3 - 4*n^2 + 10*n - 2 (n>=1). 2
6, 18, 46, 102, 198, 346, 558, 846, 1222, 1698, 2286, 2998, 3846, 4842, 5998, 7326, 8838, 10546, 12462, 14598, 16966, 19578, 22446, 25582, 28998, 32706, 36718, 41046, 45702, 50698, 56046, 61758, 67846, 74322, 81198, 88486, 96198, 104346, 112942, 121998 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For n>=2, a(n) is the first Zagreb index of the graph KK_n, defined as 2 copies of the complete graph K_n, with one vertex from one copy joined to two vertices of the other copy (see the Stevanovic et al. reference, p. 396).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of KK_n is M(KK_n; x,y) = (n-2)^2*x^{n-1}*y^{n-1}+2*(n-2)*x^{n-1}*y^n + (n-1)*x^{n-1}*y^{n+1} + x^n*y^n +2*x^n*y^{n+1}.
LINKS
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
D. Stevanovic, I. Stankovic, and M. Milosevic, More on the relation between energy and Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 61, 2009, 395-401.
FORMULA
a(n) = A033431(n-1) + A054000(n+1). - Omar E. Pol, May 09 2018
From Colin Barker, May 09 2018: (Start)
G.f.: 2*x*(3 - 3*x + 5*x^2 + x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
MATHEMATICA
Table[2n^3-4n^2+10n-2 , {n, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {6, 18, 46, 102}, 50] (* Harvey P. Dale, Oct 17 2022 *)
PROG
(PARI) Vec(2*x*(3 - 3*x + 5*x^2 + x^3) / (1 - x)^4 + O(x^60)) \\ Colin Barker, May 09 2018
CROSSREFS
Sequence in context: A261647 A305031 A031128 * A261016 A328890 A188379
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 09 2018
STATUS
approved

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Last modified April 18 09:35 EDT 2024. Contains 371779 sequences. (Running on oeis4.)