A292057 Wiener index of the n X n queen graph.

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

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