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A227497
The hyper-Wiener index of the nanostar dendrimer defined pictorially as NS_3[n] in the Ashrafi et al. references.
2
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 19 2013
STATUS
approved