OFFSET
1,1
REFERENCES
D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.
LINKS
H. P. Patil and R. Pandiya Raj, On the total graph of Mycielski graphs, central graphs and their covering numbers, Discussiones Mathematicae Graph Theory, Vol. 33 (2013), pp. 361-371.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 4*n^2 + 6*n + 5.
G.f.: x*(15-12*x+5*x^2)/(1-x)^3.
The Hosoya-Wiener polynomial is (4*n+1)*t + (2*n^2 + n + 2)*t^2.
From Elmo R. Oliveira, Nov 15 2024: (Start)
E.g.f.: exp(x)*(4*x^2 + 10*x + 5) - 5.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
EXAMPLE
a(1)=15; indeed K(1,1) is the 1-edge graph; the Mycielski construction yields the cycle C(5); its Wiener index is 5*1 + 5*2 = 15.
MAPLE
a := proc (n) options operator, arrow: 4*n^2+6*n+5 end proc; seq(a(n), n = 1 .. 38);
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {15, 33, 59}, 50] (* Harvey P. Dale, Jan 13 2022 *)
PROG
(PARI) a(n)=4*n^2+6*n+5 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Emeric Deutsch, Aug 27 2013
STATUS
approved