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A227711
The hyper-Wiener index of the nanostar dendrimer defined pictorially in Fig. 2 of the Madanshekaf reference.
2
403929, 7123491, 73556943, 584118615, 3973793223, 24439248231, 140086159911, 762624306855, 3992164666791, 20266876319655, 100389136655271, 487362872044455, 2326764524198823, 10952675858742183, 50938660677696423, 234448450914335655, 1069296992883227559
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*(254016*n^2-728028*n+1207116) + 2^n*(13104*n^2-50682*n-1250685)+48039.
G.f.: 3*x*(134643-183720*x-400012*x^2-612832*x^3+2889984*x^4 -2158592*x^5 +762880*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).
MAPLE
a := proc (n) options operator, arrow: 4^n*(254016*n^2-728028*n+1207116) +2^n*(13104*n^2-50682*n-1250685)+48039 end proc: seq(a(n), n = 1 .. 20);
MATHEMATICA
CoefficientList[Series[3 (134643 - 183720 x - 400012 x^2 - 612832 x^3 + 2889984 x^4 - 2158592 x^5 + 762880 x^6) / ((1 - x) (1 - 2 x)^3 (1 - 4 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)
PROG
(Magma) [4^n*(254016*n^2-728028*n+1207116)+2^n*(13104*n^2-50682*n-1250685)+48039: n in [1..20]]; // Vincenzo Librandi, Aug 04 2013
CROSSREFS
Cf. A227710.
Sequence in context: A157826 A215998 A186606 * A247305 A254025 A254018
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 03 2013
EXTENSIONS
Typo in the g.f. corrected from Bruno Berselli, Aug 05 2013
STATUS
approved