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A224438
The hyper-Wiener index of the nanostar dendrimer NS_1[n], defined pictorially in the A. R. Ashrafi et al. reference.
1
2083, 49057, 599137, 5290465, 38816833, 252649537, 1512820417, 8522867905, 45851773633, 237985012417, 1200461013697, 5916834366145, 28610917655233, 136152093909697, 639176875958977, 2965915539989185, 13624215530365633, 62033920525853377, 280263192943256257
OFFSET
0,1
COMMENTS
a(1) has been checked by the direct computation of the Wiener index (using Maple).
LINKS
Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512)
FORMULA
a(n) = -7487 +(-59832 - 10740n + 4200n^2)*2^n +(69402 -36480n + 14400n^2)*4^n.
G.f.: (2083 + 9480z - 20496z^2 - 59376z^3 + 217776z^4 - 422016z^5 + 70400z^6)/((1-z)(1-2z)^3*(1-4z)^3). [Corrected by Georg Fischer, May 19 2019]
MAPLE
a := proc (n) options operator, arrow: -7487-10740*2^n*n-36480*4^n*n+69402*4^n-59832*2^n+4200*2^n*n^2+14400*4^n*n^2 end proc: seq(a(n), n = 0 .. 18);
MATHEMATICA
CoefficientList[Series[(2083 + 9480z - 20496z^2 - 59376z^3 + 217776z^4 - 422016z^5 + 70400z^6)/((1-z)(1-2z)^3*(1-4z)^3), {z, 0, 18}], z] (* Georg Fischer, May 19 2019 *)
CROSSREFS
Cf. A224437.
Sequence in context: A229909 A323813 A323472 * A323714 A343179 A323750
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Apr 06 2013
STATUS
approved