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A227709
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The hyper-Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.
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3
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159, 906, 5664, 34932, 206652, 1168620, 6344268, 33264780, 169424652, 842319372, 4104041484, 19659270156, 92822679564, 432877854732, 1997218529292, 9129086189580, 41386604691468, 186264812126220, 832881548328972, 3702608701685772, 16373934411743244
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history;
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OFFSET
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0,1
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COMMENTS
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a(2) has been checked by the direct computation of the distance matrix (with Maple).
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REFERENCES
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A. Heydari, I. Gutman, On the terminal index of thorn graphs, Kragujevac J. Sci., 32, 2010, 57-64.
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LINKS
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FORMULA
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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).
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MAPLE
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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);
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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