A193399 Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).

27, 109, 271, 545, 931, 1493, 2199, 3145, 4267, 5693, 7327, 9329, 11571, 14245, 17191, 20633, 24379, 28685, 33327, 38593, 44227, 50549, 57271, 64745, 72651, 81373, 90559, 100625, 111187, 122693, 134727

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 (2,1,-4,1,2,-1).

Formula

a(n) = 4*n^3 + 16*n^2 + 8*n + 2*(-1)^n*(n - 2) - 3.

G.f.: x*(27 + 55*x + 26*x^2 + 2*x^3 - 21*x^4 + 7*x^5)/((1+x)^2*(1-x)^4). - Bruno Berselli, Jul 27 2011

Maple

a := proc (n) options operator, arrow: 4*n^3+16*n^2+8*n+2*(-1)^n*(n-2)-3 end proc: seq(a(n), n = 1 .. 40);

Prog

(Magma) [4*n^3 + 16*n^2 + 8*n + 2*(-1)^n*(n - 2) - 3: n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=4*n^3+16*n^2+8*n+2*(-1)^n*(n-2)-3 \\ Charles R Greathouse IV, Jul 28 2011

Crossrefs

Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396, A193397, A193398.

Sequence in context: A042424 A248095 A193391 * A193393 A143938 A042428

Adjacent sequences: A193396 A193397 A193398 * A193400 A193401 A193402

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2011

Status

approved