OFFSET
1,1
COMMENTS
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).
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.
EXAMPLE
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.
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);
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {42, 2697, 29805, 163914, 616008, 1819539, 4550763}, 30] (* Harvey P. Dale, Feb 11 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 31 2012
STATUS
approved