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A193396
Hyper-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).
5
215, 636, 1557, 3162, 5875, 10008, 16113, 24630, 36239, 51508, 71245, 96146, 127147, 165072, 210985, 265838, 330823, 407020, 495749, 598218, 715875, 850056, 1002337, 1174182, 1367295, 1583268, 1823933, 2091010, 2386459, 2712128, 3070105, 3462366, 3891127, 4358492
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) = (8*n^4 + 24*n^3 + 28*n^2 + 213*n + 33*(-1)^n - 246)/3.
G.f.: x^2*(215 - 224*x + 88*x^2 + 114*x^3 - 63*x^4 - 2*x^5)/((1+x)*(1-x)^5). - Bruno Berselli, Jul 27 2011
MAPLE
a := proc (n) options operator, arrow: (8/3)*n^4+8*n^3+(28/3)*n^2+71*n+11*(-1)^n-82 end proc: seq(a(n), n = 2 .. 35);
PROG
(Magma) [(8*n^4 + 24*n^3 + 28*n^2 + 213*n + 33*(-1)^n - 246)/3: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(8*n^4+24*n^3+28*n^2+213*n+33*(-1)^n-246)/3 \\ Charles R Greathouse IV, Jul 28 2011
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 25 2011
STATUS
approved