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A227497 The hyper-Wiener index of the nanostar dendrimer defined pictorially as NS_3[n] in the Ashrafi et al. references. 2
535169, 4777031, 34585827, 221183963, 1302236107, 7228350891, 38398435691, 197183359211, 985730525163, 4821548959211, 23163432305131, 109613958560235, 512102661482987, 2366223242742251, 10829048025942507, 49144438521268715, 221377260695718379 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(1) has been checked by the direct computation of the hyper-Wiener index (using Maple).

REFERENCES

A. R. Ashrafi, P. Nikzad, Connectivity index of the family of dendrimer nanostars, Digest J. Nanomaterials and Biostructures, 4, 2009, 269-273.

A. R. Ashrafi, P. Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. Nanomaterials and Biostructures, 4, 2009, 383-388.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = 2539 + 2^n*(-79425 + 368*n - 416*n^2) + 4^n*(113822 + 15808*n + 43264*n^2).

G.f.: x*(535169 - 5391180*x + 24097588*x^2 - 59759584*x^3 + 84286784*x^4 - 62611456*x^5 + 18911232*x^6) / ((1-x)*(1-2*x)^3*(1-4*x)^3).

MAPLE

aa := proc (n) options operator, arrow: 2539+2^n*(-79425+368*n-416*n^2) +4^n*(113822+15808*n+43264*n^2) end proc: seq(aa(n), n = 1 .. 20);

MATHEMATICA

CoefficientList[Series[(535169 - 5391180 x + 24097588 x^2 - 59759584 x^3 + 84286784 x^4 - 62611456 x^5 + 18911232 x^6) / ((1 - x) (1 - 2 x)^3 (1 - 4 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 20 2013 *)

PROG

(MAGMA) [2539 + 2^n*(-79425 + 368*n - 416*n^2) + 4^n*(113822 + 15808*n + 43264*n^2): n in [1..20]]; // Vincenzo Librandi, Jul 20 2013

CROSSREFS

Cf. A227496.

Sequence in context: A061730 A235076 A269322 * A183650 A273812 A210124

Adjacent sequences:  A227494 A227495 A227496 * A227498 A227499 A227500

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jul 19 2013

EXTENSIONS

Typo in g.f. fixed by Vincenzo Librandi, Jul 20 2013

STATUS

approved

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Last modified May 18 23:41 EDT 2021. Contains 344009 sequences. (Running on oeis4.)