A228597 The Wiener index of the graph obtained by applying Mycielski's construction to a benzenoid consisting of a linear chain of n hexagons.

141, 445, 941, 1629, 2509, 3581, 4845, 6301, 7949, 9789, 11821, 14045, 16461, 19069, 21869, 24861, 28045, 31421, 34989, 38749, 42701, 46845, 51181, 55709, 60429, 65341, 70445, 75741, 81229, 86909, 92781, 98845, 105101, 111549, 118189

Offset: 1

Author

Emeric Deutsch, Aug 27 2013

Keywords

• nonn
• easy

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• 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).
• B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A143937.

Programs

Magma

[96*n^2+16*n+29: n in [1..40]]; // Vincenzo Librandi, Dec 09 2016

Maple

a := proc (n) options operator, arrow: 96*n^2+16*n+29 end proc: seq(a(n), n = 1 .. 35);

Mathematica

LinearRecurrence[{3, -3, 1}, {141, 445, 941}, 100] (* or *) Table[96*n^2 + 16*n + 29 , {n,1,100}] (* G. C. Greubel, Dec 08 2016 *)

PARI

Vec(x*(141+22*x+29*x^2)/(1-x)^3 + O(x^50)) \\ G. C. Greubel, Dec 08 2016

Formula

a(n) = 96*n^2 + 16*n + 29.

G.f.: x*(141+22*x+29*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - G. C. Greubel, Dec 08 2016