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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
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^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);
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {55, 133, 259, 442}, 40] (* Harvey P. Dale, Mar 18 2023 *)
CROSSREFS
Cf. A224460.
Sequence in context: A039442 A063324 A046156 * A218161 A044306 A044687
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 29 2013
STATUS
approved