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A224459 The Wiener index of the straight pentachain of n pentagonal rings (see Fig. 2.1 in the A. A. Ali et al. reference). 1
55, 133, 259, 442, 691, 1015, 1423, 1924, 2527, 3241, 4075, 5038, 6139, 7387, 8791, 10360, 12103, 14029, 16147, 18466, 20995, 23743, 26719, 29932, 33391, 37105, 41083, 45334, 49867, 54691, 59815, 65248, 70999, 77077, 83491, 90250, 97363, 104839, 112687 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

REFERENCES

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

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

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

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

LINKS

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

FORMULA

a(n) = (3*n^3 +21*n^2 -6*n +14)/2.

G.f.: z^2*(55-87*z+57*z^2-16*z^3)/(1-z)^4.

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: (3/2)*n^3+(21/2)*n^2-3*n+7 end proc: seq(a(n), n = 2 .. 40);

CROSSREFS

Cf. A224460.

Sequence in context: A039442 A063324 A046156 * A218161 A044306 A044687

Adjacent sequences:  A224456 A224457 A224458 * A224460 A224461 A224462

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jun 29 2013

STATUS

approved

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Last modified May 7 09:58 EDT 2021. Contains 343649 sequences. (Running on oeis4.)