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Revision History for A227709

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A227709

The hyper-Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.
(history; published version)

#11 by Charles R Greathouse IV at Thu Sep 08 08:46:05 EDT 2022

PROG

(MAGMAMagma) [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

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#10 by Ralf Stephan at Mon Aug 05 03:25:26 EDT 2013

STATUS

reviewed

approved

#9 by Bruno Berselli at Mon Aug 05 03:05:05 EDT 2013

STATUS

proposed

reviewed

#8 by Bruno Berselli at Mon Aug 05 03:05:01 EDT 2013

STATUS

editing

proposed

#7 by Bruno Berselli at Mon Aug 05 03:04:57 EDT 2013

FORMULA

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).

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

STATUS

proposed

editing

#6 by Vincenzo Librandi at Sun Aug 04 13:47:45 EDT 2013

STATUS

editing

proposed

#5 by Vincenzo Librandi at Sun Aug 04 13:47:29 EDT 2013

LINKS

Vincenzo Librandi, <a href="/A227709/b227709.txt">Table of n, a(n) for n = 0..1000</a>

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.

STATUS

approved

editing

#4 by Joerg Arndt at Sat Aug 03 04:25:07 EDT 2013

STATUS

proposed

approved

#3 by Emeric Deutsch at Fri Aug 02 19:29:28 EDT 2013

STATUS

editing

proposed

#2 by Emeric Deutsch at Fri Aug 02 19:29:19 EDT 2013

NAME

allocated for Emeric DeutschThe hyper-Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.

DATA

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.

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);

CROSSREFS

Cf. A227707, A227708

KEYWORD

allocated

nonn,easy

AUTHOR

Emeric Deutsch, Aug 02 2013

STATUS

approved

editing