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 A216111 The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 2
 42, 477, 1953, 5442, 12240, 23967, 42567, 70308, 109782, 163905, 235917, 329382, 448188, 596547, 778995, 1000392, 1265922, 1581093, 1951737, 2384010, 2884392, 3459687, 4117023, 4863852, 5707950, 6657417, 7720677, 8906478, 10223892, 11682315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Hosoya-Wiener polynomial of the graph is n(6+6t+6t^2+3t^3)+(1+2t+2t^2+t^3)^2*(t^{3n+1}-nt^4+nt-t)/(t^3-1)^2. REFERENCES Y. Dou, H. Bian, H. Gao, and H. Yu, The polyphenyl chains with extremal edge-Wiener indices, MATCH Commun. Math. Comput. Chem., 64, 2010, 757-766. LINKS H. Deng, Wiener indices of spiro and polyphenyl hexagonal chains, arXiv:1006.5488 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = 3*n*(-13+14*n+18*n^2+9*n^3)/2. G.f.: -3*x*(9*x^3-4*x^2+89*x+14)/(x-1)^5. [Colin Barker, Oct 30 2012] MAPLE seq(3*n*(9*n^3+18*n^2+14*n-13)*(1/2), n=1..30); CROSSREFS Cf. A216108, A216109, A216110, A216112, A216113. Sequence in context: A088626 A328175 A216109 * A216113 A204566 A249233 Adjacent sequences:  A216108 A216109 A216110 * A216112 A216113 A216114 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Oct 26 2012 EXTENSIONS Typo corrected in first formula by Colin Barker, Oct 30 2012 STATUS approved

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Last modified December 8 12:25 EST 2019. Contains 329862 sequences. (Running on oeis4.)