OFFSET
1,2
COMMENTS
Sequence extended to a(2) using the formula/recurrence (the graph is disconnected for n = 2).
LINKS
Eric Weisstein's World of Mathematics, Rook Complement 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^2*(n + 3)/2.
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*(-5 - 2*x + x^2)/(-1 + x)^5.
From Amiram Eldar, Apr 16 2022: (Start)
Sum_{n>=2} 1/a(n) = 265/216 - Pi^2/9.
Sum_{n>=2} (-1)^n/a(n) = Pi^2/18 + 8*log(2)/9 - 233/216. (End)
MATHEMATICA
Table[(n - 1) n^2 (n + 3)/2, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 10, 54, 168, 400}, 20]
CoefficientList[Series[2 x (-5 - 2 x + x^2)/(-1 + x)^5, {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 08 2017
STATUS
approved