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A193390 The hyper-Wiener index of a benzenoid consisting of a straight-line chain of n hexagons (s=2; see the Gutman et al. reference). 1
42, 215, 680, 1661, 3446, 6387, 10900, 17465, 26626, 38991, 55232, 76085, 102350, 134891, 174636, 222577, 279770, 347335, 426456, 518381, 624422, 745955, 884420, 1041321, 1218226, 1416767, 1638640, 1885605, 2159486, 2462171, 2795612, 3161825, 3562890, 4000951, 4478216 (list; graph; refs; listen; history; text; internal format)
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 + 32*n^3 + 46*n^2 + 37*n + 3)/3.

The Wiener-Hosoya polynomial is W(n,t) = (2*(t+1)*t^(2*n+2) - t^3 - 2*t^2 - 3*t + n*(t-1)*(t^2+1)*(t^2-t-4)+2)/(1-t)^2.

G.f.: x*(42 + 5*x + 25*x^2 - 9*x^3 + x^4)/(1-x)^5. - Bruno Berselli, Jul 27 2011

MAPLE

a := proc (n) options operator, arrow: (8/3)*n^4+(32/3)*n^3+(46/3)*n^2+(37/3)*n+1 end proc; seq(a(n), n = 1 .. 35);

PROG

(MAGMA) [(8*n^4 + 32*n^3 + 46*n^2 + 37*n + 3)/3: n in [1..30]]; // Vincenzo Librandi, Jul 26 2011

(PARI) a(n)=(8*n^4+32*n^3+46*n^2+37*n)/3+1 \\ Charles R Greathouse IV, Jul 26 2011

CROSSREFS

Cf. A143937, A143938.

Sequence in context: A193392 A193400 A193394 * A154472 A221523 A263304

Adjacent sequences:  A193387 A193388 A193389 * A193391 A193392 A193393

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jul 25 2011

STATUS

approved

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Last modified July 1 07:15 EDT 2022. Contains 354952 sequences. (Running on oeis4.)