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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
LINKS
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 29 2013
STATUS
approved

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Last modified April 16 07:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)