OFFSET
1,1
COMMENTS
a(1) has been checked by the direct computation of the Wiener index (using Maple).
The Deutsch et al. reference contains also the Hosoya polynomial of D_n.
LINKS
E. Deutsch and S. Klavzar, Computing the Hosoya polynomial of graphs from primary subgraphs, MATCH Commun. Math. Comput. Chem., 70, 2013, 627-644.
M. Ghorbani, A. Mohammadi, and F. Madadi, Some topological indices of nanostar dendrimers, Optoelectronics and Adv. Materials - Rapid Comm., 4, 2010, 1871-1873.
M. Ghorbani and M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.
Index entries for linear recurrences with constant coefficients, signature (15,-86,232,-288,128).
FORMULA
a(n) = 116340 - 2^n*1429983/2 + 4^n*4790367/8 - 4^n*2685555*n/8 + 4^n*263169*n^2/4.
From Chai Wah Wu, Mar 11 2021: (Start)
a(n) = 15*a(n-1) - 86*a(n-2) + 232*a(n-3) - 288*a(n-4) + 128*a(n-5) for n > 5.
G.f.: x*(-18480*x^4 - 1099524*x^3 - 1744632*x^2 - 276612*x - 1932)/((x - 1)*(2*x - 1)*(4*x - 1)^3). (End)
MAPLE
a := proc (n) options operator, arrow: 116340-1429983*2^(n-1)+4790367*2^(2*n-3)-2685555*2^(2*n-3)*n+263169*2^(2*n-2)*n^2 end proc: seq(a(n), n = 1 .. 20);
PROG
(Python)
def A227491(n): return 2**n*(2**n*(526338*n**2 - 2685555*n + 4790367) - 5719932)//8 + 116340 # Chai Wah Wu, Mar 11 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 16 2013
EXTENSIONS
Incorrect g.f. removed by Georg Fischer, Apr 17 2020
STATUS
approved