A227484 The Wiener index of the dendrimer D_4[n], defined pictorially in the A. R. Ashrafi et al. reference.

426, 110582, 1543242, 12208658, 76176642, 419676194, 2147525346, 10478078306, 49478563938, 228185184866, 1033790121570, 4619196304994, 20412418326114, 89390811225698, 388524258582114, 1677932514369122, 7207051830287970, 30809448121032290, 131162651106926178, 556349805776789090, 2352195514241310306

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..20.

Formula

a(n) = -74142 + 2^n*(241658-45756*n)+4^n*(115320*n - 167090).

G.f.: 2*(213 +52522*z + 66470*z^2 -419644*z^3-33200*z^4)/((1-z)*(1-2*z)^2*(1-4*z)^2).

Maple

a := proc (n) options operator, arrow: -74142+2^n*(241658-45756*n)+4^n*(115320*n-167090) end proc: seq(a(n), n = 0 .. 20);

Crossrefs

Cf. A227485

Sequence in context: A236699 A338154 A173374 * A272131 A054984 A251147

Adjacent sequences: A227481 A227482 A227483 * A227485 A227486 A227487

Keyword

nonn

Author

Emeric Deutsch, Jul 13 2013

Status

approved