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

1,1

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