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A292053
Wiener index of the n X n king graph.
1
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
Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Wiener Index
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 08 2017
STATUS
approved