

A213820


Principal diagonal of the convolution array A213819.


5



2, 18, 60, 140, 270, 462, 728, 1080, 1530, 2090, 2772, 3588, 4550, 5670, 6960, 8432, 10098, 11970, 14060, 16380, 18942, 21758, 24840, 28200, 31850, 35802, 40068, 44660, 49590, 54870, 60512, 66528, 72930, 79730
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OFFSET

1,1


COMMENTS

Every term is even: a(n) = 2*A002414(n).
a(n) is the first Zagreb index of the graph obtained by joining one vertex of a complete graph K[n] with each vertex of a second complete graph K[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph.  Emeric Deutsch, Nov 07 2016


REFERENCES

I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 8392.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

a(n) = n + n^2 + 2*n^3.
a(n) = 4*a(n1)  6*a(n2) + 4*a(n3)  a(n4).
G.f.: f(x)/g(x), where f(x) = 2*x*(1 + 5*x) and g(x) = (1x)^4.


MATHEMATICA

(See A213819.)


CROSSREFS

Cf. A213819.
Sequence in context: A114109 A085293 A119118 * A078837 A232155 A112365
Adjacent sequences: A213817 A213818 A213819 * A213821 A213822 A213823


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jul 04 2012


STATUS

approved



