A193396 Hyper-Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).

215, 636, 1557, 3162, 5875, 10008, 16113, 24630, 36239, 51508, 71245, 96146, 127147, 165072, 210985, 265838, 330823, 407020, 495749, 598218, 715875, 850056, 1002337, 1174182, 1367295, 1583268, 1823933, 2091010, 2386459, 2712128, 3070105, 3462366, 3891127, 4358492

Offset

2,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..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 (4,-5,0,5,-4,1).

Formula

a(n) = (8*n^4 + 24*n^3 + 28*n^2 + 213*n + 33*(-1)^n - 246)/3.

G.f.: x^2*(215 - 224*x + 88*x^2 + 114*x^3 - 63*x^4 - 2*x^5)/((1+x)*(1-x)^5). - Bruno Berselli, Jul 27 2011

Maple

a := proc (n) options operator, arrow: (8/3)*n^4+8*n^3+(28/3)*n^2+71*n+11*(-1)^n-82 end proc: seq(a(n), n = 2 .. 35);

Prog

(Magma) [(8*n^4 + 24*n^3 + 28*n^2 + 213*n + 33*(-1)^n - 246)/3: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(8*n^4+24*n^3+28*n^2+213*n+33*(-1)^n-246)/3 \\ Charles R Greathouse IV, Jul 28 2011

Crossrefs

Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395.

Sequence in context: A043391 A063358 A193398 * A259889 A362201 A137205

Adjacent sequences: A193393 A193394 A193395 * A193397 A193398 A193399

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2011

Status

approved