OFFSET
3,1
COMMENTS
The n-sunlet graph is the graph on 2n vertices obtained by attaching a pendant edge to each vertex of the cycle graph C_n.
REFERENCES
M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science, 2001, Huntington, N.Y. p. 151.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 3..1000
Eric Weisstein's World of Mathematics, Sunlet Graph.
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = 4*n*(floor(n/2))^2 +2*n^2 - n.
a(n) = n^3 if n is odd; a(n) = n^3 + 2*n^2 -n if n is even.
G.f.: x^3*(27+65*x-48*x^2-38*x^3+43*x^4+13*x^5-14*x^6)/((1+x)^3*(1-x)^4).
If we attach r pendant edges to each vertex of the cycle graph C_n, then the obtained graph has Szeged index n(r+1)^2*(floor(n/2))^2 +(nr)^2 + n^2*r - nr.
MAPLE
a := proc (n) options operator, arrow: 4*n*floor((1/2)*n)^2+2*n^2-n end proc: seq(a(n), n = 3 .. 38);
MATHEMATICA
Table[If[OddQ[n], n^3, n^3+2n^2-n], {n, 3, 40}] (* or *) LinearRecurrence[ {1, 3, -3, -3, 3, 1, -1}, {27, 92, 125, 282, 343, 632, 729}, 40] (* Harvey P. Dale, Jul 23 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 16 2013
STATUS
approved