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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
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
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 03 2013
STATUS
approved