A224459 The Wiener index of the straight pentachain of n pentagonal rings (see Fig. 2.1 in the A. A. Ali et al. reference).

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

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 (4,-6,4,-1).

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

Adjacent sequences: A224456 A224457 A224458 * A224460 A224461 A224462

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 29 2013

Status

approved