A277980 -id:A277980 - cp's OEIS frontend

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

Offset: 0

Emeric Deutsch, Nov 08 2016

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}.
4*a(n) + 81 is a square. - Bruno Berselli, May 08 2018

			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.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A139576, A277980.

Subsequence of A028569.

[4*n^2+18*n: n in [0..50]]; // Vincenzo Librandi, Nov 09 2016

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

Table[4 n^2 + 18 n, {n, 0, 50}] (* Vincenzo Librandi, Nov 09 2016 *)
LinearRecurrence[{3,-3,1},{0,22,52},50] (* Harvey P. Dale, Mar 01 2022 *)

a(n)=4*n^2+18*n \\ Charles R Greathouse IV, Jun 17 2017

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).

cp's OEIS Frontend

A277979 a(n) = 4n^2 + 18n.

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