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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). 2
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 (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 (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

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Last modified January 28 14:26 EST 2022. Contains 350656 sequences. (Running on oeis4.)