A193392 Hyper-Wiener index of a benzenoid consisting of a spiral chain of n hexagons (s=1; see the Gutman et al. reference).

42, 215, 636, 1401, 2622, 4427, 6960, 10381, 14866, 20607, 27812, 36705, 47526, 60531, 75992, 94197, 115450, 140071, 168396, 200777, 237582, 279195, 326016, 378461, 436962, 501967, 573940, 653361, 740726, 836547, 941352, 1055685, 1180106, 1315191, 1461532

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) = (2*n^4 + 28*n^3 + 154*n^2 - 169*n + 111)/3.

G.f.: x*(42 + 5*x - 19*x^2 - 49*x^3 + 37*x^4)/(1-x)^5. - Bruno Berselli, Jul 27 2011

Maple

a := proc (n) options operator, arrow; (2/3)*n^4+(28/3)*n^3+(154/3)*n^2-(169/3)*n+37 end proc: seq(a(n), n = 1 .. 35);

Prog

(Magma) [(2*n^4 + 28*n^3 + 154*n^2 - 169*n + 111)/3: n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
(PARI) a(n)=(2*n^4+28*n^3+154*n^2-169*n)/3+37 \\ Charles R Greathouse IV, Jul 26 2011

Crossrefs

Cf. A143937, A143938, A193391.

Sequence in context: A008446 A255424 A122232 * A193400 A193394 A193390

Adjacent sequences: A193389 A193390 A193391 * A193393 A193394 A193395

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2011

Status

approved