OFFSET
0,2
COMMENTS
For n > 1, also the number of irredundant sets in the complete bipartite graph K_{n,n}.
For n > 1, also the number of irredundant sets in the 2 X n rook graph. - Andrew Howroyd, Aug 11 2017
LINKS
Eric Weisstein's World of Mathematics, Complete Bipartite Graph.
Eric Weisstein's World of Mathematics, Irredundant Set.
Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).
FORMULA
a(n) = 2^(n+1) + n^2 - 1.
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
G.f.: x*(1 - x - 2*x^3)/((-1 + x)^3*(-1 + 2*x)).
E.g.f.: exp(x)*(x^2 + x - 1 + 2*exp(x)). - Elmo R. Oliveira, Mar 06 2025
MATHEMATICA
Table[2^(n + 1) + n^2 - 1, {n, 0, 40}]
LinearRecurrence[{5, -9, 7, -2}, {4, 11, 24, 47}, {0, 20}]
CoefficientList[Series[(1 - x - 2 x^3)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]
PROG
(PARI) a(n)=2^(n+1)+n^2-1 \\ Charles R Greathouse IV, Aug 09 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Eric W. Weisstein, Aug 09 2017
STATUS
approved