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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).
3
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
2,1
LINKS
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.
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
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);
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 *)
PROG
(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
(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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 25 2011
STATUS
approved