OFFSET
0,2
COMMENTS
For n>=3, a(n) is the second Zagreb index of the double-wheel graph DW[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.
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
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).
FORMULA
EXAMPLE
a(3) = 162. 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 second Zagreb index is 6*9 + 6*18 = 162.
MAPLE
seq(12*n^2+18*n, n = 0 .. 50);
MATHEMATICA
Table[12 n^2 + 18 n, {n, 0, 45}] (* Vincenzo Librandi, Nov 09 2016 *)
PROG
(Magma) [12*n^2+18*n: n in [0..40]]; // Vincenzo Librandi, Nov 09 2016
(PARI) a(n)=12*n^2+18*n \\ Charles R Greathouse IV, Nov 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 08 2016
STATUS
approved