

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
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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 Mpolynomial of KK_n is M(KK_n; x,y) = (n2)^2*x^{n1}*y^{n1}+2*(n2)*x^{n1}*y^n + (n1)*x^{n1}*y^{n+1} + x^n*y^n +2*x^n*y^{n+1}.


LINKS



FORMULA

G.f.: 2*x*(3  3*x + 5*x^2 + x^3) / (1  x)^4.
a(n) = 4*a(n1)  6*a(n2) + 4*a(n3)  a(n4) for n>4.
(End)


MATHEMATICA

Table[2n^34n^2+10n2 , {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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



