A193390 The hyper-Wiener index of a benzenoid consisting of a straight-line chain of n hexagons (s=2; see the Gutman et al. reference).
42, 215, 680, 1661, 3446, 6387, 10900, 17465, 26626, 38991, 55232, 76085, 102350, 134891, 174636, 222577, 279770, 347335, 426456, 518381, 624422, 745955, 884420, 1041321, 1218226, 1416767, 1638640, 1885605, 2159486, 2462171, 2795612, 3161825, 3562890, 4000951, 4478216
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..10000
- A. A. Dobrynin, I. Gutman, S. Klavzar, 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 (5,-10,10,-5,1).
Programs
-
Magma
[(8*n^4 + 32*n^3 + 46*n^2 + 37*n + 3)/3: n in [1..30]]; // Vincenzo Librandi, Jul 26 2011
-
Maple
a := proc (n) options operator, arrow: (8/3)*n^4+(32/3)*n^3+(46/3)*n^2+(37/3)*n+1 end proc; seq(a(n), n = 1 .. 35);
-
PARI
a(n)=(8*n^4+32*n^3+46*n^2+37*n)/3+1 \\ Charles R Greathouse IV, Jul 26 2011
Formula
a(n) = (8*n^4 + 32*n^3 + 46*n^2 + 37*n + 3)/3.
The Wiener-Hosoya polynomial is W(n,t) = (2*(t+1)*t^(2*n+2) - t^3 - 2*t^2 - 3*t + n*(t-1)*(t^2+1)*(t^2-t-4)+2)/(1-t)^2.
G.f.: x*(42 + 5*x + 25*x^2 - 9*x^3 + x^4)/(1-x)^5. - Bruno Berselli, Jul 27 2011