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A227710 The Wiener index of the nanostar dendrimer defined pictorially in Fig. 2 of the Madanshekaf reference. 2
47160, 501516, 3609684, 21645828, 117137700, 594466020, 2889375588, 13620124260, 62765849700, 284277930084, 1270122831972, 5612855201892, 24581542031460, 106848038187108, 461482510708836, 1982297444839524 (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).

REFERENCES

A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, 2011, 1075-1080.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = 4^n*(31752*n-46494)+2^n*(3276*n+51786)-3996.

G.f.: 36*x*(1310-3099*x+3006*x^2-4520*x^3+2304*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2).

MAPLE

a := proc (n) options operator, arrow: 4^n*(31752*n-46494)+2^n*(3276*n+51786)-3996 end proc: seq(a(n), n = 1 .. 20);

MATHEMATICA

CoefficientList[Series[36 (1310 - 3099 x + 3006 x^2 - 4520 x^3 + 2304 x^4) / ((1 - x) (1 - 2 x)^2 (1 - 4 x)^2), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 04 2013 *)

PROG

(Magma) [(4^n*(31752*n-46494)+2^n*(3276*n+51786))-3996: n in [1..20]]; // Vincenzo Librandi, Aug 04 2013

CROSSREFS

Cf. A227711.

Sequence in context: A254549 A254556 A254479 * A215840 A257723 A320621

Adjacent sequences: A227707 A227708 A227709 * A227711 A227712 A227713

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Aug 03 2013

STATUS

approved

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Last modified February 4 22:05 EST 2023. Contains 360082 sequences. (Running on oeis4.)