A227711 The hyper-Wiener index of the nanostar dendrimer defined pictorially in Fig. 2 of the Madanshekaf reference.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..300

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

Adjacent sequences: A227708 A227709 A227710 * A227712 A227713 A227714

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 03 2013

Extensions

Typo in the g.f. corrected from Bruno Berselli, Aug 05 2013

Status

approved