

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*(1310*x)/(1x)^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



