A214580 The hyper-Wiener index of the circumcoronene H(n) (see definition in the Klavzar papers).
42, 2697, 29805, 163914, 616008, 1819539, 4550763, 10075380, 20321478, 38078781, 67224201, 112973694, 182160420, 283539207, 428117319, 629511528, 904331490, 1272589425, 1758136101, 2389123122, 3198491520, 4224486651, 5511199395, 7109133660, 9075800190, 11476336677, 14384154177
Offset: 1
Examples
a(1)=42: for n=1 we have a hexagon; the distances are: 1 (6 times), 2 (6 times), 3 (3 times). Then a(1)=(1/2)*(6*1+6*2+3*3+6*1+6*4+3*9)=42.
Links
- S. Klavzar, A bird's eye view of the cut method and a survey of its applications in chemical graph theory, MATCH, Commun. Math. Comput. Chem. 60, 2008, 255-274.
- Bo-Yin Yang and Yeong-Nan Yeh, A Crowning Moment for Wiener Indices, Studies in Appl. Math., 112 (2004), 333-340.
- P. Zigert, S. Klavzar, and I. Gutman, Calculating the hyper-Wiener index of benzenoid hydrocarbons, ACH Models Chem., 137, 2000, 83-94.
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Maple
a := proc (n) options operator, arrow: (1/10)*n+(17/15)*n^2-3*n^3-(55/6)*n^4+(82/5)*n^5+(548/15)*n^6 end proc: seq(a(n), n = 1 .. 30);
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Mathematica
LinearRecurrence[{7,-21,35,-35,21,-7,1},{42,2697,29805,163914,616008,1819539,4550763},30] (* Harvey P. Dale, Feb 11 2024 *)
Formula
a(n) = (1/10)n +(17/15)n^2 -3n^3 -(55/6)n^4 +(82/5)n^5 +(548/15)n^6.
G.f. = 3*x*(14 +801*x +3936*x^2 +3482*x^3 +530*x^4 +5*x^5)/(1-x)^7.
Comments