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A292057 Wiener index of the n X n queen graph. 0
0, 6, 44, 164, 440, 970, 1876, 3304, 5424, 8430, 12540, 17996, 25064, 34034, 45220, 58960, 75616, 95574, 119244, 147060, 179480, 216986, 260084, 309304, 365200, 428350, 499356, 578844, 667464, 765890, 874820, 994976, 1127104, 1271974, 1430380, 1603140, 1791096, 1995114 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, Queen Graph

Eric Weisstein's World of Mathematics, Wiener Index

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = (n - 1)*n*(3*n^2 - 2*n + 1)/3.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: 2*x^2*(3 + 7*x + 2*x^2)/(1 - x)^5.

MATHEMATICA

Table[(n - 1) n (3 n^2 - 2 n + 1)/3, {n, 20}]

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 6, 44, 164, 440}, 20]

CoefficientList[Series[2 x (3 + 7 x + 2 x^2)/(1 - x)^5, {x, 0, 20}], x]

CROSSREFS

Sequence in context: A114074 A075337 A000561 * A258156 A182540 A309418

Adjacent sequences:  A292054 A292055 A292056 * A292058 A292059 A292060

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Sep 08 2017

STATUS

approved

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Last modified October 3 17:29 EDT 2022. Contains 357237 sequences. (Running on oeis4.)