Non-Fisherian generalized Fibonacci numbers

Using biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered. We demonstrate that the generalized Fibonacci numbers being investigated are generalized third order Pell–Lucas numbers. Sequence properties, generating functions, and closed-form solutions for these new generalized Fibonacci numbers, as well as several identities involving Jacobsthal, Leonardo, and generalized Leonardo numbers are presented. The generalized Fibonacci number framework developed gives rise to many previously uncataloged sequences, and develops new connections between known sequences.