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A193395
Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).
6
109, 271, 553, 971, 1573, 2375, 3425, 4739, 6365, 8319, 10649, 13371, 16533, 20151, 24273, 28915, 34125, 39919, 46345, 53419, 61189, 69671, 78913, 88931, 99773, 111455, 124025, 137499, 151925, 167319, 183729, 201171, 219693, 239311, 260073, 281995, 305125, 329479, 355105
OFFSET
2,1
LINKS
A. A. Dobrynin, I. Gutman, S. Klavzar, and P. Zigert, Wiener Index of Hexagonal Systems, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
FORMULA
a(n) = (16*n^3 + 24*n^2 + 74*n +6*(-1)^n - 51)/3.
G.f.: x^2*(109 - 56*x - 42*x^2 + 72*x^3 - 19*x^4)/((1+x)*(1-x)^4). - Bruno Berselli, Jul 27 2011
MAPLE
a := proc (n) options operator, arrow; (16/3)*n^3+8*n^2+(74/3)*n+2*(-1)^n-17 end proc: seq(a(n), n = 2 .. 40);
MATHEMATICA
Table[(16n^3+24n^2+74n+6(-1)^n-51)/3, {n, 2, 40}] (* or *) LinearRecurrence[ {3, -2, -2, 3, -1}, {109, 271, 553, 971, 1573}, 40] (* Harvey P. Dale, Apr 08 2020 *)
PROG
(Magma) [(16*n^3 + 24*n^2 + 74*n +6*(-1)^n - 51)/3: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(16*n^3+24*n^2+74*n+6*(-1)^n)/3-17 \\ Charles R Greathouse IV, Jul 28 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 25 2011
STATUS
approved