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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 (list; graph; refs; listen; history; text; internal format)
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, 83-92.

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(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: f(x)/g(x), where f(x) = 2*x*(1 + 5*x) and g(x) = (1-x)^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

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Last modified December 17 04:09 EST 2017. Contains 296096 sequences.