A216111 The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).

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

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

Table of n, a(n) for n=1..30.

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 A348833

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