A224460 The hyper-Wiener index of the straight pentachain of n pentagonal rings (see Fig. 2.1 in the A. A. Ali et al. reference).

91, 263, 589, 1126, 1940, 3106, 4708, 6839, 9601, 13105, 17471, 22828, 29314, 37076, 46270, 57061, 69623, 84139, 100801, 119810, 141376, 165718, 193064, 223651, 257725, 295541, 337363, 383464, 434126, 489640, 550306, 616433, 688339, 766351, 850805, 942046, 1040428, 1146314, 1260076

Offset

2,1

Links

Table of n, a(n) for n=2..40.

A. A. Ali and A. M. Ali, Hosoya polynomials of pentachains, Comm. Math. Comp. Chem. (MATCH), 65, 2011, 807-819.

I. Gutman, W. Yan, Y.-N. Yeh, and B.-Y. Yang, Generalized Wiener indices of zigzagging pentachains, J. Math. Chem., 42, 2007, 103-117.

O. Halakoo, O. Khormali, and A. Mahmiani, Bounds for Schultz index of pentachains, Digest J. Nanomaterials and Biostructures, 4, 2009, 687-691.

N. P. Rao and A. L. Prasanna, On the Wiener index of pentachains, Applied Math. Sci., 2, 2008, 2443-2457.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (3*n^4 +34*n^3 +145*n^2 -190*n +208)/8.

G.f.: z^2*(91-192*z+184*z^2-99*z^3+25*z^4)/(1-z)^5.

The Hosoya polynomial is [t - 4t^2 - 3t^3 - 2t^5 - 3t^6 + 2t^7 + 4nt - nt^2 - 3nt^3 + nt^5 - nt^7 + t^{n+2} + 4t^{n+3} + 4t^{n+4}](t-1)^2.

Maple

a := proc (n) options operator, arrow: (3/8)*n^4+(17/4)*n^3+(145/8)*n^2-(95/4)*n+26 end proc: seq(a(n), n = 2 .. 40);

Crossrefs

Cf. A224459.

Sequence in context: A051973 A290812 A000864 * A350206 A020441 A209255

Adjacent sequences: A224457 A224458 A224459 * A224461 A224462 A224463

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 29 2013

Status

approved