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A228597
The Wiener index of the graph obtained by applying Mycielski's construction to a benzenoid consisting of a linear chain of n hexagons.
1
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
1,1
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).
B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.
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
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 *)
PROG
(PARI) Vec(x*(141+22*x+29*x^2)/(1-x)^3 + O(x^50)) \\ G. C. Greubel, Dec 08 2016
(Magma) [96*n^2+16*n+29: n in [1..40]]; // Vincenzo Librandi, Dec 09 2016
CROSSREFS
Cf. A143937.
Sequence in context: A031892 A063373 A145192 * A255154 A068046 A186954
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 27 2013
STATUS
approved