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The case (k=3) of this corollary is given by Q'_{3}(n)=frac{1- -1)^{n}}{2} biggllfloor frac{n}{4} biggrrfloor -delta_{0,(n-3) operatorname{mod}6 }-delta_{0,(n-1) operatorname{mod}2},quad n geqslant7.

On the other hand, if there are units that test each other, a third diagnosability condition is formulated in replacement of (c2) [14], for which a corollary is given: (c3) let G be a digraph of a system of n units; if κ(G) ≥t then the system is t-diagnosable, where κ(G) stands for the connectivity of G, i.e., the minimum number of vertices whose removal disconnects G [10].

The following corollary was given by Pettet and Sitaramachandrarao [11].

The following corollary was given in [15] on page 123 by Sedghi and Dung.

The proof of Corollary 4.1 is given in the Appendix.

A generalization of [[2], Corollary 3.3] is given in the next result.

(i) Note that a valid λ ⋆ in Corollary 3.2 ii) is given by formula (3.8).

Then the transfer formula [7, Corollary 3.8.2] is given by q n ( x ) = x ( f ( t ) g ( t ) ) n x − 1 p n ( x ) ( n ≥ 1 ).

Remark 1 In the above results by taking ψ = ω, we obtain Corollary 3.2, which is given in [2].

In [1], the following corollary of Theorem 4 is given.

A weaker result (a corollary of Lemma 1) is given in [[16], p.154].