A253926 a(n) is the excess of the number of Collatz permutations of length n (with first index 15) over the n-th Fibonacci number.

1, 2, 3, 3, 4, 6, 7, 9, 12, 15, 19, 24, 30, 39, 49, 61, 77, 96

Offset: 15

Author

William J. Keith, Jan 19 2015

Keywords

• nonn
• more

Comments

A permutation is Collatz if for some n it is the sequence of ranks of terms prior to a power of 2 generated by the Collatz function C(n) = n/2 if n even, (3n+1) if n odd. For instance, iteration of the Collatz function on 12 generates 12, 6, 3, 10, 5, which is then followed by 16, so (5,3,1,4,2) is Collatz. Among n = 1 to 14, the number of Collatz permutations is the n-th Fibonacci number; thereafter, there is an increasing excess. This sequence counts the excess.

Links

• Michael Albert, Bjarki Gudmundsson and Henning Ulfarsson, Collatz meets Fibonacci. arXiv:1404.3054 [math.CO], 2014-2015. Table on page 4.

Crossrefs

A000045, the Fibonacci numbers, gives the number of Collatz permutations for n <= 14.