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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
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Queen Graph
Eric Weisstein's World of Mathematics, Wiener Index
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 08 2017
STATUS
approved