A227485 The hyper-Wiener index of the dendrimer D_4[n], defined pictorially in the A. R. Ashrafi et al. reference.

1165, 795061, 19190411, 222761135, 1865766759, 13037931735, 81350611063, 470142180535, 2571969023543, 13504663462199, 68693896897335, 340717322458935, 1655620816211767, 7909483093294903, 37250047530671927, 173305467651546935, 797871121068613431, 3639796169374261047

Offset

0,1

Comments

a(1) has been checked by the direct computation of the 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..17.

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

Formula

a(n) = 1007415 + 2^n*(-4509545 + 732099*n - 171585*n^(2)) + 4^n*(3503295 -2446768*n + 864900*n^(2)).

G.f.: (1165 + 772926*z + 4259002*z^2 - 23338464*z^3 + 8025448*z^4 + 35155008*z^5 + 2325120*z^6)/((1-z)*(1-2*z)^3*(1-4*z)^3).

Maple

a := proc (n) options operator, arrow: 1007415+2^n*(-4509545+732099*n-171585*n^2)+4^n*(3503295-2446768*n+864900*n^2) end proc: seq(a(n), n = 0 .. 20);

Crossrefs

Cf. A227484

Sequence in context: A223800 A244428 A221350 * A252009 A032744 A185477

Adjacent sequences: A227482 A227483 A227484 * A227486 A227487 A227488

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 13 2013

Status

approved