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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. 2
1932, 305592, 6162360, 67702236, 555929988, 3858461844, 24038223540, 139011929844, 761612920692, 4005957732468, 20412297267828, 101407748443764, 493489861416564, 2360705148118644, 11131067755529844, 51842363941865076, 238902338228766324 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 10:04 EST 2022. Contains 350598 sequences. (Running on oeis4.)