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A277976 a(n) = n*(3*n + 23). 0
0, 26, 58, 96, 140, 190, 246, 308, 376, 450, 530, 616, 708, 806, 910, 1020, 1136, 1258, 1386, 1520, 1660, 1806, 1958, 2116, 2280, 2450, 2626, 2808, 2996, 3190, 3390, 3596, 3808, 4026, 4250, 4480, 4716, 4958, 5206, 5460, 5720, 5986, 6258, 6536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n >= 3, a(n) is the second Zagreb index of the graph obtained by joining one vertex of the cycle graph C[n] with each vertex of a second cycle graph C[n].

The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.

LINKS

Table of n, a(n) for n=0..43.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: 2*x*(13-10*x)/(1-x)^3.

EXAMPLE

a(4) = 140. Indeed, the corresponding graph has 12 edges. We list the degrees of their endpoints: (2,2), (2,2), (2,6), (2,6), (3,3), (3,3), (3,3), (3,3), (3,6), (3,6), (3,6), (3,6). Then, the second Zagreb index is 4 + 4 + 12 + 12 + 9 + 9 + 9 + 9 + 18 + 18 + 18 + 18 = 140.

MAPLE

seq(n*(3*n+23), n = 0..50);

MATHEMATICA

Table[n(3n+23), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 26, 58}, 50] (* Harvey P. Dale, Sep 30 2017 *)

PROG

(PARI) a(n)=n*(3*n+23) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A132761.

Sequence in context: A245004 A161341 A038861 * A291105 A267294 A162316

Adjacent sequences:  A277973 A277974 A277975 * A277977 A277978 A277979

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 07 2016

STATUS

approved

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Last modified December 14 21:33 EST 2017. Contains 296020 sequences.