A224457 The hyper-Wiener index of the cyclic phenylene with n hexagons (n>=3).

1062, 2760, 5715, 10386, 17304, 27072, 40365, 57930, 80586, 109224, 144807, 188370, 241020, 303936, 378369, 465642, 567150, 684360, 818811, 972114, 1145952, 1342080, 1562325, 1808586, 2082834, 2387112, 2723535, 3094290

Offset

3,1

Comments

a(3), a(4), ..., a(16) have been checked by the direct computation of the hyper-Wiener index (using Maple).

References

Y. Alizadeh, S. Klavzar, The Wiener dimension of a graph (unpublished manuscript).

Links

Table of n, a(n) for n=3..30.

G. Cash, S. Klavzar, M. Petkovsek, Three methods for calculation of the hyper-Wiener index of a molecular graph, J. Chem. Inf. Comput. Sci. 42, 2002, 571-576.

Formula

a(n) = (3/2)n(2n^3 +15n^2 + 45n -88).

G.f.: 3z^3(354-850z+845z^2-403z^3+78z^4)/(1-z)^5.

The Hosoya polynomial of the cyclic phenylene with n hexagons is [n*t^n*(t^5+3t^4+5t^3+5t^2+3t+1) - n(t^8+t^7+t^6+t^5+2t^3+4t^2+8t)]/(t-1).

Maple

a := proc (n) options operator, arrow: (3/2)*n*(2*n^3+15*n^2+45*n-88) end proc: seq(a(n), n = 3 .. 35);

Mathematica

Table[(3n(2n^3+15n^2+45n-88))/2, {n, 3, 30}] (* Harvey P. Dale, Mar 02 2018 *)

Crossrefs

Cf. A224456.

Sequence in context: A172384 A177136 A080334 * A123211 A023078 A056102

Adjacent sequences: A224454 A224455 A224456 * A224458 A224459 A224460

Keyword

nonn

Author

Emeric Deutsch, Apr 14 2013

Status

approved