A216113 The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).

42, 477, 2241, 6846, 16380, 33507, 61467, 104076, 165726, 251385, 366597, 517482, 710736, 953631, 1254015, 1620312, 2061522, 2587221, 3207561, 3933270, 4775652, 5746587, 6858531, 8124516, 9558150, 11173617, 12985677, 15009666, 17261496, 19757655

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^{4n+1}-nt^5+nt-t)/(t^4-1)^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) = 3n(16n^3 + 8n^2 - 5n +9)/2.

G.f.: 3*x*(3*x^3-92*x^2-89*x-14)/(x-1)^5. [Colin Barker, Oct 30 2012]

Maple

seq(3*n*(16*n^3+8*n^2-5*n+9)*(1/2), n=1..30);

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {42, 477, 2241, 6846, 16380}, 30] (* Jean-François Alcover, Sep 23 2017 *)

Crossrefs

Cf. A216108-A216112.

Sequence in context: A328175 A216109 A216111 * A204566 A348833 A249233

Adjacent sequences: A216110 A216111 A216112 * A216114 A216115 A216116

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 26 2012

Status

approved