OFFSET
1,1
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).
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
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);
PROG
(Magma) [(8*n^4 + 32*n^3 + 46*n^2 + 37*n + 3)/3: n in [1..30]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(8*n^4+32*n^3+46*n^2+37*n)/3+1 \\ Charles R Greathouse IV, Jul 26 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 25 2011
STATUS
approved