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These denominators generate an elliptic divisibility sequence, a genus-1 analogue of more classical sequences such as Fibonacci or Mersenne, and the hypothesis, which they
r -bonacci numbers; there are sequences in both families that grow at different rates (the Fibonacci sequence, the Tanny sequence, and an eventually constant sequence can all occur as
Here, we find recurrence relations for the Hankel transform of more general linear combinations of Catalan numbers, involving up to four adjacent Catalan numbers, with
These numbers are also called the Bernoulli numbers of the second kind, and are represented by sequences A006232 and A006233 in Sloane’s Encyclopedia.. The Cauchy numbers play
Horadam, Generating functions for powers of a certain generalised sequence of numbers, Duke Math.. Pita, More on Fibonomials, Proceedings of the XIV Conference on
Witu la, S lota and Warzy´ nski [9] analyzed the relationships between the so-called quasi- Fibonacci numbers of order 7... It follows from the
It was observed by Louis Shapiro that the Catalan numbers, the Young numbers and the powers of 2 count certain card shuffles in the paper by Robbins and Boelker [RB81], but the
Hence, second order Lucas numbers are also “hidden” in a triangle like the second order Fibonacci numbers, the difference is that now instead of the Pascal triangle we have a
