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 A193394 Hyper-Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference). 7
 42, 215, 636, 1513, 3118, 5787, 9920, 15981, 24498, 36063, 51332, 71025, 95926, 126883, 164808, 210677, 265530, 330471, 406668, 495353, 597822, 715435, 849616, 1001853, 1173698, 1366767, 1582740, 1823361, 2090438, 2385843, 2711512, 3069445, 3461706, 3890423, 4357788 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems, Acta Applicandae Mathematicae 72 (2002), pp. 247-294. I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = (8*n^4 + 24*n^3 + 28*n^2 + 147*n - 81)/3. G.f.: x*(42 + 5*x - 19*x^2 + 63*x^3 - 27*x^4)/(1-x)^5. - Bruno Berselli, Jul 27 2011 MAPLE a := n-> (8/3)*n^4+8*n^3+(28/3)*n^2+49*n-27: seq(a(n), n = 1 .. 35); MATHEMATICA LinearRecurrence[{5, -10, 10, -5, 1}, {42, 215, 636, 1513, 3118}, 40] (* Harvey P. Dale, Dec 10 2021 *) PROG (MAGMA) [(8*n^4 + 24*n^3 + 28*n^2 + 147*n - 81)/3: n in [1..40]]; // Vincenzo Librandi, Jul 26 2011 (PARI) a(n)=(8*n^2+24*n+28)*n^2/3+49*n-27 \\ Charles R Greathouse IV, Jul 28 2011 CROSSREFS Cf. A143937, A143938, A193391, A193392, A193393. Sequence in context: A122232 A193392 A193400 * A193390 A154472 A221523 Adjacent sequences:  A193391 A193392 A193393 * A193395 A193396 A193397 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jul 25 2011 STATUS approved

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Last modified June 29 15:27 EDT 2022. Contains 354913 sequences. (Running on oeis4.)