A216109 The hyper-Wiener index of the ortho-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).

42, 477, 1701, 4254, 8820, 16227, 27447, 43596, 65934, 95865, 134937, 184842, 247416, 324639, 418635, 531672, 666162, 824661, 1009869, 1224630, 1471932, 1754907, 2076831, 2441124, 2851350, 3311217, 3824577, 4395426, 5027904, 5726295

Offset

0,1

Comments

The Hosoya-Wiener polynomial of the graph is n(6+6t+6t^2+3t^3)+(1+2t+2t^2+t^3)^2*(t^{2n+1}-nt^3+nt-t)/(t^2-1)^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=0..29.

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*(28+123*n+127*n^2+36*n^3+4*n^4)/2 = 3*(n+1)(4*n^3+32*n^2+95*n+28)/2.

G.f.: -3*(33*x^3-88*x^2+89*x+14)/(x-1)^5. [Colin Barker, Oct 29 2012]

Maple

seq(3*n*(4*n^3+20*n^2+43*n-39)*(1/2), n=1..30);

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {42, 477, 1701, 4254, 8820}, 30] (* Jean-François Alcover, Sep 23 2017 *)

Crossrefs

Cf. A216108, A216110-A216113.

Sequence in context: A008387 A088626 A328175 * A216111 A216113 A204566

Adjacent sequences: A216106 A216107 A216108 * A216110 A216111 A216112

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 26 2012

Extensions

First formula corrected by Colin Barker, Oct 29 2012

Status

approved