A292053 Wiener index of the n X n king graph.

0, 6, 52, 228, 708, 1778, 3864, 7560, 13656, 23166, 37356, 57772, 86268, 125034, 176624, 243984, 330480, 439926, 576612, 745332, 951412, 1200738, 1499784, 1855640, 2276040, 2769390, 3344796, 4012092, 4781868, 5665498, 6675168, 7823904, 9125600, 10595046

Offset: 1

Author

Eric W. Weisstein, Sep 08 2017

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, King Graph
• Eric Weisstein's World of Mathematics, Wiener Index
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

Mathematica

Table[(n - 1) n (n + 1) (7 n^2 + 2)/30, {n, 40}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 6, 52, 228, 708, 1778}, 20]
CoefficientList[Series[2 x (3 + 8 x + 3 x^2)/(1 - x)^6, {x, 0, 20}], x]

Formula

a(n) = (n - 1)*n*(n + 1)*(7*n^2 + 2)/30.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

G.f.: 2*x^2*(3 + 8*x + 3*x^2)/(1 - x)^6.