login
A193400
Hyper-Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).
1
42, 215, 636, 1513, 2862, 5211, 8352, 13229, 19314, 28063, 38532, 52785, 69366, 91043, 115752, 147061, 182202, 225639, 273804, 332153, 396222, 472555, 555696, 653373, 759042, 881711, 1013652, 1165249, 1327494, 1512243, 1709112, 1931525, 2167626, 2432503, 2712732
OFFSET
1,1
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 +40*n^3 +114*n^2 +16*n -45 +(-1)^n*(6*n^2 +20*n -63) )/4.
G.f.: x*(42+131*x+122*x^2+63*x^3-146*x^4+25*x^5+78*x^6-27*x^7)/((1+x)^3*(1-x)^5). - Bruno Berselli, Jul 27 2011
MAPLE
a := proc (n) options operator, arrow: (3/2)*n^4+10*n^3+(57/2)*n^2+4*n-45/4+(1/4)*(-1)^n*(6*n^2+20*n-63) end proc: seq(a(n), n = 1 .. 35);
PROG
(Magma) [(6*n^4 + 40*n^3 + 114*n^2 + 16*n - 45 + (-1)^n*(6*n^2 +20*n -63))/4: n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(6*n^4+40*n^3+114*n^2+16*n-45+(-1)^n*(6*n^2+20*n-63))/4 \\ Charles R Greathouse IV, Jul 28 2011
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 25 2011
STATUS
approved