A227491 The hyper-Wiener index of the nanostar dendrimer D_n, defined pictorially in the Ghorbani et al. references and recursively in the Deutsch et al. reference.

1932, 305592, 6162360, 67702236, 555929988, 3858461844, 24038223540, 139011929844, 761612920692, 4005957732468, 20412297267828, 101407748443764, 493489861416564, 2360705148118644, 11131067755529844, 51842363941865076, 238902338228766324

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

Table of n, a(n) for n=1..17.

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

Cf. A227490.

Sequence in context: A166393 A141593 A221015 * A277943 A251945 A340843

Adjacent sequences: A227488 A227489 A227490 * A227492 A227493 A227494

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 16 2013

Extensions

Incorrect g.f. removed by Georg Fischer, Apr 17 2020

Status

approved