Appearance of Balancing and related number sequences in steady state probabilities of some Markov chains
Asim Patra, G. K. Panda · arXiv (Cornell University) · 2019
Balancing and Lucas-balancing numbers are solutions of a Diophantine equation and satisfy a second order homogeneous recurrence relation. Interestingly, these numbers can be seen as numerators and denominators in the steady state probabilities of a class of transition probability matrices of Markov chains. An identity relating the balancing numbers and the silver ratio can be obtained as a byproduct.