A227497 The hyper-Wiener index of the nanostar dendrimer defined pictorially as NS_3[n] in the Ashrafi et al. references.

535169, 4777031, 34585827, 221183963, 1302236107, 7228350891, 38398435691, 197183359211, 985730525163, 4821548959211, 23163432305131, 109613958560235, 512102661482987, 2366223242742251, 10829048025942507, 49144438521268715, 221377260695718379

Offset

1,1

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..201 [Offset shifted to 1 by Georg Fischer, Aug 19 2021]

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

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

Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).

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: A344944 A344945 A269322 * A183650 A273812 A210124

Adjacent sequences: A227494 A227495 A227496 * A227498 A227499 A227500

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 19 2013

Status

approved