Catalan Numbers, Lucas numbers, and Circuits

Abstract

Shapiro [8] asked what simple family of circuits will have resistances \(C_{2n}/{C_{2n}-1}\) (or something similar) where \(C_m=\frac{1}{m+1}\binom{2m}{m}\) is the \(m\)th Catalan number. In this paper, we give a construction of such circuits; we also discuss some related problems.