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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n>=3, a(n) is the first Zagreb index of the double-wheel 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 double-wheel graph DW[n] consists of two cycles C[n], whose vertices are connected to an additional vertex.

The M-polynomial of the double-wheel graph DW[n] is M(DW[n],x,y)= 2*n*x^3*y^3 + 2*n*x^3*y^{2*n}.

LINKS

Table of n, a(n) for n=0..47.

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

a(n) = 2*A139576(n).

EXAMPLE

a(3) = 90. Indeed, the double-wheel graph DW[3] has 6 edges with end-point degrees 3,3 and 6 edges with end-point 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: A191279 A200880 A111576 * A177726 A101571 A290381

Adjacent sequences:  A277976 A277977 A277978 * A277980 A277981 A277982

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 08 2016

STATUS

approved

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Last modified December 13 01:33 EST 2017. Contains 295954 sequences.