A227706 The hyper-Wiener index of the nanostar dendrimer defined pictorially as G(n) in the Darafsheh et al. reference.

477, 16515, 222975, 2038455, 15095079, 98153991, 584951751, 3276557127, 17527771719, 90505289799, 454449839175, 2230961075271, 10750358250567, 51003115291719, 238802012701767, 1105498179306567, 5067682186396743, 23031604974453831, 103882403285042247

Offset

0,1

Comments

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

References

M. R. Darafsheh, M. H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Comb., 100, 2011, 289-298.

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (15,-86,232,-288,128).

Formula

a(n) = 4^n*(5184*n^2 - 10368*n + 18696) - 2^n*19314 + 1095.

G.f.: 9*(53 +1040*x + 1808*x^2 +384*x^3)/((1-x)*(1-2*x)*(1-4*x)^3).

Maple

a := proc (n) options operator, arrow: 4^n*(5184*n^2-10368*n+18696)-19314*2^n+1095 end proc: seq(a(n), n = 0 .. 22);

Mathematica

LinearRecurrence[{15, -86, 232, -288, 128}, {477, 16515, 222975, 2038455, 15095079}, 20] (* Harvey P. Dale, Nov 09 2022 *)

Crossrefs

Cf. A227705.

Sequence in context: A216141 A325822 A224453 * A261816 A352265 A020375

Adjacent sequences: A227703 A227704 A227705 * A227707 A227708 A227709

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 29 2013

Status

approved