A227708 The Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.

84, 354, 1674, 8178, 39858, 191250, 900498, 4164114, 18952722, 85106706, 377862162, 1661755410, 7249502226, 31410683922, 135299432466, 579837493266, 2473936945170, 10514155438098, 44530379784210, 188016821796882, 791649070350354

Offset

0,1

Comments

a(2) has been checked by the direct computation of the distance matrix (with Maple).

References

A. Heydari, I. Gutman, On the terminal index of thorn graphs, Kragujevac J. Sci., 32, 2010, 57-64.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (13,-64,148,-160,64).

Formula

a(n) = 18 + 2^n*(66+30*n) + 36*n*4^n.

G.f.: 6*(14-123*x+408*x^2-560*x^3+288*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2).

a(0)=84, a(1)=354, a(2)=1674, a(3)=8178, a(4)=39858, a(n)=13*a(n-1)- 64*a(n-2)+ 148*a(n-3)- 160*a(n-4)+64*a(n-5). - Harvey P. Dale, Jan 09 2016

Maple

a := proc (n) options operator, arrow: 18+2^n*(66+30*n)+36*4^n*n end proc: seq(a(n), n = 0 .. 25);

Mathematica

CoefficientList[Series[6 (14 - 123 x + 408 x^2 - 560 x^3 + 288 x^4) / ((1 - x) (1 - 2 x)^2 (1 - 4 x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 04 2013 *)
LinearRecurrence[{13, -64, 148, -160, 64}, {84, 354, 1674, 8178, 39858}, 30] (* Harvey P. Dale, Jan 09 2016 *)

Prog

(Magma) [18+2^n*(66+30*n)+36*n*4^n: n in [0..25]]; // Vincenzo Librandi, Aug 04 2013

Crossrefs

Cf. A227707, A227709.

Sequence in context: A131072 A210645 A241612 * A229537 A083986 A189543

Adjacent sequences: A227705 A227706 A227707 * A227709 A227710 A227711

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 02 2013

Extensions

Typo in formula fixed by Vincenzo Librandi, Aug 04 2013

Status

approved