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A180576 Wiener index of the n-web graph. 1
4, 27, 69, 148, 255, 417, 616, 888, 1206, 1615, 2079, 2652, 3289, 4053, 4890, 5872, 6936, 8163, 9481, 10980, 12579, 14377, 16284, 18408, 20650, 23127, 25731, 28588, 31581, 34845, 38254, 41952, 45804, 49963, 54285, 58932, 63751, 68913, 74256, 79960 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The n-web graph is the stacked prism graph C_n X P_3 with the edges of the outer cycle removed.

Equivalently, the n-web graph is obtained by attaching a pendant edge to each node of the outer cycle of the circular ladder (prism) C_n X P_2.

The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.

a(n) = sum(A180575(n,k), k>=1).

Sequence extended to a(1)-a(2) using the formula/recurrence. - Eric W. Weisstein, Sep 08 2017

REFERENCES

B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.

LINKS

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Web Graph

Eric Weisstein's World of Mathematics, Wiener Index

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

a(2n) = n*(9*n^2+20*n-2); a(2n+1) = (2*n+1)*(9*n^2+29*n+8)/2.

G.f.: -x^3*(27*x^5-50*x^4-35*x^3+110*x^2-10*x-69)/((x-1)^4*(x+1)^2). - Colin Barker, Oct 31 2012

a(n) = n*(2*n*(9*n+40)+9*(-1)^n-25)/16. - Bruno Berselli, Oct 31 2012

MAPLE

a := proc (n) if `mod`(n, 2) = 1 then (1/8)*n*(9*n^2+40*n-17) else (1/8)*n*(9*n^2+40*n-8) end if end proc: seq(a(n), n = 3 .. 45);

MATHEMATICA

Table[n (-25 + 9 (-1)^n + 2 n (40 + 9 n))/16, {n, 20}] (* Eric W. Weisstein, Sep 08 2017 *)

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {4, 27, 69, 148, 255, 4178}, 20] (* Eric W. Weisstein, Sep 08 2017 *)

CoefficientList[Series[(4 + 19 x + 11 x^2 - x^3 - 6 x^4 + 3761 x^5)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 08 2017 *)

CROSSREFS

Cf. A180575

Sequence in context: A294038 A175701 A227866 * A158186 A272858 A272818

Adjacent sequences:  A180573 A180574 A180575 * A180577 A180578 A180579

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Sep 19 2010

EXTENSIONS

a(1)-a(2) from Eric W. Weisstein, Sep 08 2017

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)