A193398 Hyper-Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n >= 2, s = 21; see the Gutman et al. reference).
215, 636, 1557, 3018, 5555, 8968, 14225, 20790, 30159, 41364, 56525, 74146, 97067, 123168, 156105, 193038, 238535, 288940, 349829, 416634, 496035, 582456, 683777, 793318, 920255, 1056708, 1213245, 1380690, 1571099, 1773904, 2002745, 2245566, 2517687, 2805468
Offset: 2
Links
- Vincenzo Librandi, Table of n, a(n) for n = 2..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 (2,2,-6,0,6,-2,-2,1).
Programs
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Magma
[(3/2)*n^4+12*n^3+(3/2)*n^2*(-1)^n+(73/2)*n^2+6*n*(-1)^n-79*n+(83/4)*(-1)^(n+1)+439/4: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011
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Maple
a := n -> (3/2)*n^4+12*n^3+(3/2)*n^2*(-1)^n+(73/2)*n^2+6*n*(-1)^n-79*n+(83/4)*(-1)^(n+1)+439/4: seq(a(n), n = 2 .. 35);
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Mathematica
LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{215,636,1557,3018,5555,8968,14225,20790},40] (* Harvey P. Dale, Aug 30 2017 *) -
PARI
a(n)=(6*n^4+48*n^3+146*n^2-316*n+439+(-1)^n*(6*n^2+24*n-83))/4 \\ Charles R Greathouse IV, Jul 28 2011
Formula
a(n) = (6*n^4 + 48*n^3 + 146*n^2 - 316*n + 439 + (-1)^n*(6*n^2 + 24*n - 83))/4.
G.f.: x^2*(215 + 206*x - 145*x^2 - 78*x^3 + 221*x^4 - 126*x^5 - 99*x^6 + 94*x^7)/((1+x)^3*(1-x)^5). - Bruno Berselli, Jul 26 2011