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).
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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 2..10000
- 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.
- Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
Programs
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Magma
[(16*n^3 + 24*n^2 + 74*n +6*(-1)^n - 51)/3: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011
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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);
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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 *) -
PARI
a(n)=(16*n^3+24*n^2+74*n+6*(-1)^n)/3-17 \\ Charles R Greathouse IV, Jul 28 2011
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