OFFSET
1,1
COMMENTS
When n > 1, the nonempty irredundant sets are those consisting of either any number of vertices from a single partition or otherwise exactly two vertices from different partitions. - Andrew Howroyd, Aug 10 2017
LINKS
Eric Weisstein's World of Mathematics, Complete Tripartite 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) = 3*(2^n + n^2) - 2 for n > 1. - Andrew Howroyd, Aug 10 2017
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n > 5.
G.f.: (x (4 + 2 x - 25 x^2 + 19 x^3 - 6 x^4))/((-1 + x)^3 (-1 + 2 x)).
MATHEMATICA
Table[If[n == 1, 4, 3 (2^n + n^2) - 2], {n, 20}]
Join[{4}, LinearRecurrence[{5, -9, 7, -2}, {22, 49, 94, 169}, 20]]
CoefficientList[Series[(4 + 2 x - 25 x^2 + 19 x^3 - 6 x^4)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]
PROG
(PARI) a(n) = if(n==1, 4, 3*(2^n + n^2) - 2); \\ Andrew Howroyd, Aug 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 09 2017
EXTENSIONS
a(7)-a(32) from Andrew Howroyd, Aug 10 2017
STATUS
approved