

A277978


a(n) = 3n(n+3).


1



0, 12, 30, 54, 84, 120, 162, 210, 264, 324, 390, 462, 540, 624, 714, 810, 912, 1020, 1134, 1254, 1380, 1512, 1650, 1794, 1944, 2100, 2262, 2430, 2604, 2784, 2970, 3162, 3360, 3564, 3774, 3990, 4212, 4440, 4674, 4914, 5160, 5412, 5670, 5934, 6204, 6480
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OFFSET

0,2


COMMENTS

For n>= 3, a(n) is the second Zagreb index of the wheel graph with n+1 vertices. The second Zagreb index of a simple connected graph 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..45.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 2 * A140091(n) = 3 * A028552(n) = 6 * A000096(n).
G.f.: 6*x*(2x)/(1x)^3


EXAMPLE

a(3) = 54. Indeed, the wheel graph with 4 vertices consists of 6 edges, each connecting two vertices of degree 3. Then, the second Zagreb index is 6*3*3 = 54.


MAPLE

seq(3*n*(n+3), n = 0 .. 45);


MATHEMATICA

A277978[n_] := 3 n (n + 3); Array[A277978, 45] (* JungHwan Min, Nov 08 2016 *)


PROG

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


CROSSREFS

Cf. A000096, A028569, A140091.
Sequence in context: A031107 A019557 A173107 * A131874 A111396 A080385
Adjacent sequences: A277975 A277976 A277977 * A277979 A277980 A277981


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, Nov 08 2016


STATUS

approved



