A193394 Hyper-Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).

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

Offset: 1

Author

Emeric Deutsch, Jul 25 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A143937, A143938, A193391, A193392, A193393.

Programs

Magma

[(8*n^4 + 24*n^3 + 28*n^2 + 147*n - 81)/3: n in [1..40]]; // Vincenzo Librandi, Jul 26 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 *)

PARI

a(n)=(8*n^2+24*n+28)*n^2/3+49*n-27 \\ Charles R Greathouse IV, Jul 28 2011

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