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

1,2

Links

Table of n, a(n) for n=1..34.

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).

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.

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]

Crossrefs

Sequence in context: A165896 A080265 A357428 * A202925 A287082 A007974

Adjacent sequences: A292050 A292051 A292052 * A292054 A292055 A292056

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 08 2017

Status

approved