

A277979


a(n) = 4*n^2 + 18*n.


1



0, 22, 52, 90, 136, 190, 252, 322, 400, 486, 580, 682, 792, 910, 1036, 1170, 1312, 1462, 1620, 1786, 1960, 2142, 2332, 2530, 2736, 2950, 3172, 3402, 3640, 3886, 4140, 4402, 4672, 4950, 5236, 5530, 5832, 6142, 6460, 6786, 7120, 7462, 7812, 8170, 8536, 8910, 9292, 9682
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OFFSET

0,2


COMMENTS

For n>=3, a(n) is the first Zagreb index of the doublewheel graph DW[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.
The doublewheel graph DW[n] consists of two cycles C[n], whose vertices are connected to an additional vertex.
The Mpolynomial of the doublewheel graph DW[n] is M(DW[n],x,y)= 2*n*x^3*y^3 + 2*n*x^3*y^{2*n}.
4*a(n) + 81 is a square.  Bruno Berselli, May 08 2018


LINKS

Table of n, a(n) for n=0..47.
E. Deutsch and Sandi Klavzar, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

O.g.f.: 2*x*(11  7*x)/(1  x)^3.
E.g.f.: 2*x*(11 + 2*x)*exp(x).
a(n) = 3*a(n1)  3*a(n2) + a(n3).
a(n) = 2*A139576(n).


EXAMPLE

a(3) = 90. Indeed, the doublewheel graph DW[3] has 6 edges with endpoint degrees 3,3 and 6 edges with endpoint degrees 3,6. Then the first Zagreb index is 6*6 + 6*9 = 90.


MAPLE

seq(4*n^2+18*n, n = 0..50);


MATHEMATICA

Table[4 n^2 + 18 n, {n, 0, 50}] (* Vincenzo Librandi, Nov 09 2016 *)


PROG

(MAGMA) [4*n^2+18*n: n in [0..50]]; // Vincenzo Librandi, Nov 09 2016
(PARI) a(n)=4*n^2+18*n \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A139576, A277980.
Subsequence of A028569.
Sequence in context: A200880 A330409 A111576 * A177726 A101571 A290381
Adjacent sequences: A277976 A277977 A277978 * A277980 A277981 A277982


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, Nov 08 2016


STATUS

approved



