APPEARANCE OF BALANCING AND RELATED NUMBER SEQUENCES IN STEADY STATE PROBABILITIES OF SOME MARKOV CHAINS

摘要

The balancing numbers x and the Lucas-balancing numbers y are solutions of the Diophantine equation 8x2 + 1 = y2, and both types of numbers satisfy a common second order recurrence relation. These numbers can be seen as numerators and denominators in the steady state probabilities of a class of Markov chains.