A224430 The hyper-Wiener index of the dendrimer D_1[n], defined pictorially in the A. R. Ashrafi et al. reference.

159, 104448, 2123802, 22761810, 183445458, 1256801106, 7758199698, 44564150802, 242917046802, 1272665857554, 6464520301074, 32033885569554, 155562155893266, 742852590887442, 3497424488243730, 16268164668891666, 74884202558956050, 341573770043761170, 1545606217427624466

Offset

0,1

Comments

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

References

A. R. Ashrafi and H. Shabani, Computing Padmakar-Ivan index of four classes of dendrimers, Bulgarian Chem. Comm., 44, N0. 2, 2012, 127-130.

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).

Formula

a(n) = 41490 - 420000*2^n + 81225*4^n*n^2 - 467115*4^n*n/2 + 378669*4^n + 231*2^n*n - 1425*2^n*n^2.

G.f. = 3(53+33809z+54380z^2-674784z^3+1120160z^4-847120z^5+686912z^6)/[(1-z)(1-2z)^3*(1-4z)^3].

Maple

a := proc (n) options operator, arrow: 41490-420000*2^n+81225*4^n*n^2-(467115/2)*4^n*n+378669*4^n+231*2^n*n-1425*2^n*n^2 end proc: seq(a(n), n = 0 .. 18);

Crossrefs

Cf. A224429

Sequence in context: A268029 A263518 A213695 * A013454 A013455 A013465

Adjacent sequences: A224427 A224428 A224429 * A224431 A224432 A224433

Keyword

nonn,easy

Author

Emeric Deutsch, Apr 06 2013

Status

approved