A227495 The hyper-Wiener index of the nanostar dendrimer D_n, defined pictorially as NS[n] in the Yang et al. reference.

4797, 135138, 2268072, 25678020, 224320572, 1649999532, 10785747852, 64824941388, 366263505612, 1974734612940, 10266404558796, 51852359848908, 255825084304332, 1238033348475852, 5895322649598924, 27690990109023180, 128550270229863372, 590735658025999308

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