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A227495 The hyper-Wiener index of the nanostar dendrimer D_n, defined pictorially as NS[n] in the Yang et al. reference. 1
4797, 135138, 2268072, 25678020, 224320572, 1649999532, 10785747852, 64824941388, 366263505612, 1974734612940, 10266404558796, 51852359848908, 255825084304332, 1238033348475852, 5895322649598924, 27690990109023180, 128550270229863372, 590735658025999308 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(2) has been checked by the direct computation of the Wiener index (using Maple).

REFERENCES

L. Yang, Connectivity, PI and vertex-Pi indices and polynomials of an infinite class of dendrimer nanostars, International J. Physical Sciences, 7(9), 2012, 1420-1423.

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) = - 140340 + 2^n*(82764*n^2 - 268092*n - 1159017) + 4^n*(156816*n^2 - 719928*n + 1304154).

G.f.: 3*(1599 + 14665*x + 140000*x^2 - 65180*x^3 - 605152*x^4 -886208*x^5 + 137216*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).

MAPLE

a := proc (n) options operator, arrow: -140340+2^n*(82764*n^2-268092*n-1159017)+4^n*(156816*n^2-719928*n+1304154) end proc: seq(a(n), n = 0 .. 22);

CROSSREFS

Cf. A227494.

Sequence in context: A251775 A096517 A221005 * A254035 A255412 A254791

Adjacent sequences:  A227492 A227493 A227494 * A227496 A227497 A227498

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jul 17 2013

STATUS

approved

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Last modified May 7 19:23 EDT 2021. Contains 343652 sequences. (Running on oeis4.)