OFFSET
0,2
COMMENTS
Also the number of independent vertex sets in the n X n rook complement graph. - Eric W. Weisstein, Sep 11 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Clique.
Eric Weisstein's World of Mathematics, Independent Vertex Set.
Eric Weisstein's World of Mathematics, Rook Complement Graph.
Eric Weisstein's World of Mathematics, Rook Graph.
Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).
FORMULA
a(n) = 1 + 2*n*(2^n - 1) - n^2.
a(n) = 7*a(n-1) - 19*a(n-2) + 25*a(n-3) - 16*a(n-4) + 4*a(n-5).
G.f.: (1 - 5*x + 14*x^2 - 16*x^3 + 4*x^4)/((1 - x)^3*(1 - 2*x)^2).
E.g.f.: exp(x)*(4*x*exp(x) + (1 - 3*x - x^2)). - Elmo R. Oliveira, Sep 17 2025
MATHEMATICA
LinearRecurrence[{7, -19, 25, -16, 4}, {2, 9, 34, 105, 286}, 20]
Table[1 + 2 n (2^n - 1) - n^2, {n, 20}]
CoefficientList[Series[(2 - 5 x + 9 x^2 - 12 x^3 + 4 x^4)/((1 - x)^3 (1 - 2 x)^2), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 20 2017
EXTENSIONS
a(0) = 1 prepended by Andrew Howroyd, May 22 2025
STATUS
approved
