A228321 The Wiener index of the graph obtained by applying Mycielski's construction to the path graph on n vertices (n>=2).

15, 33, 62, 103, 156, 221, 298, 387, 488, 601, 726, 863, 1012, 1173, 1346, 1531, 1728, 1937, 2158, 2391, 2636, 2893, 3162, 3443, 3736, 4041, 4358, 4687, 5028, 5381, 5746, 6123, 6512, 6913, 7326, 7751, 8188, 8637, 9098, 9571, 10056, 10553, 11062

Offset: 2

Author

Emeric Deutsch, Aug 27 2013

Keywords

• nonn
• easy

Examples

			a(2)=15 because the Mycielskian of the 1-edge graph is the cycle graph C(5) with Wiener index 5*1+5*2 = 15.
		

References

• D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.

Links

• R. Balakrishnan, S. F. Raj, The Wiener number of powers of the Mycielskian, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).
• Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Programs

Maple

a := proc (n) if n = 2 then 15 else 6*n^2-13*n+18 end if end proc: seq(a(n), n = 2 .. 45);

Formula

a(2)=15; a(n) = 6n^2 - 13n + 18 (n>=3).

G.f.: x^2*(15-12*x+8*x^2+x^3)/(1-x)^3.