A227709 The hyper-Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.

159, 906, 5664, 34932, 206652, 1168620, 6344268, 33264780, 169424652, 842319372, 4104041484, 19659270156, 92822679564, 432877854732, 1997218529292, 9129086189580, 41386604691468, 186264812126220, 832881548328972, 3702608701685772, 16373934411743244

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

Formula

a(n) = 12+2^n*(15+45*n+15*n^2) + 4^n*(132+18*n+36*n^2).

G.f.: 3*(53-705*x+4100*x^2-12636*x^3+21456*x^4-19328*x^5+7168*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).

Maple

a := proc (n) options operator, arrow: 12+2^n*(15+45*n+15*n^2)+4^n*(132+18*n+36*n^2) end proc: seq(a(n), n = 0 .. 23);

Mathematica

CoefficientList[Series[3 (53 - 705 x + 4100 x^2 - 12636 x^3 + 21456 x^4 - 19328 x^5 + 7168 x^6) / ((1 - x) (1 - 2 x)^3 (1 - 4 x)^3), {x, 0, 25}], x] (* Vincenzo Librandi, Aug 04 2013 *)

Prog

(Magma) [12+2^n*(15+45*n+15*n^2)+4^n*(132+18*n+36*n^2): n in [0..25]]; // Vincenzo Librandi, Aug 04 2013

Crossrefs

Cf. A227707, A227708.

Sequence in context: A280971 A090948 A242115 * A212780 A232408 A121800

Adjacent sequences: A227706 A227707 A227708 * A227710 A227711 A227712

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 02 2013

Status

approved