Note on a Combinatorial Identity in the Theory of Bi-Colored Graphs
H. W. Gould · The Fibonacci Quarterly · 1967
In connection with an enumeration problem arising in the theory of labelled bi-colored graphs, Ce Y. Lee [2] has obtained the following identities. Defining N(a,b;n) by the expansion ab a v (1) 2> a, b; n) x n = £ -Z2>' » = Z Z f(iJ) • j=oi=o i=o j = where . = the smallest integer>x, Lee was able to show that from which as a special case he deduced the apparently novel formula It may be of interest therefore, to point out that the formulas may be written in much simpler form inasmuch as the introduction of leads to