A216112 The Wiener index of the para-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).

27, 198, 657, 1548, 3015, 5202, 8253, 12312, 17523, 24030, 31977, 41508, 52767, 65898, 81045, 98352, 117963, 140022, 164673, 192060, 222327, 255618, 292077, 331848, 375075, 421902, 472473, 526932, 585423, 648090

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 (4,-6,4,-1).

Formula

a(n) = 3n(1+8n^2).

G.f.: 9*x*(x+3)*(3*x+1)/(x-1)^4. [Colin Barker, Oct 30 2012]

Example

a(1)=27 because the graph consists of 1 hexagon and its Wiener index is 6*1+6*2+3*3=27.

Maple

seq(24*n^3+3*n, n=1..30);

Crossrefs

Cf. A216108-A216113.

Sequence in context: A042416 A216108 A216110 * A183596 A033544 A224874

Adjacent sequences: A216109 A216110 A216111 * A216113 A216114 A216115

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 26 2012

Status

approved