A329768 Number of finite sequences of positive integers whose sum minus runs-resistance is n.

8, 17, 42, 104, 242, 541, 1212, 2664, 5731, 12314

Offset

1,1

Comments

A composition of n is a finite sequence of positive integers with sum n.

For the operation of taking the sequence of run-lengths of a finite sequence, runs-resistance is defined as the number of applications required to reach a singleton.

Links

Table of n, a(n) for n=1..10.

Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003.

Example

The a(1) = 8 and a(2) = 17 compositions whose sum minus runs-resistance is n:
  (1)        (2)
  (1,1)      (1,3)
  (1,2)      (3,1)
  (2,1)      (1,1,1)
  (1,1,2)    (1,1,3)
  (2,1,1)    (1,2,1)
  (1,1,2,1)  (1,2,2)
  (1,2,1,1)  (2,2,1)
             (3,1,1)
             (1,1,1,2)
             (1,1,3,1)
             (1,3,1,1)
             (2,1,1,1)
             (1,1,1,2,1)
             (1,2,1,1,1)
             (1,2,1,1,2)
             (2,1,1,2,1)

Crossrefs

Column sums of A329750.

Cf. A000740, A008965, A098504, A242882, A318928, A329744, A329745, A329746, A329747, A329767.

Sequence in context: A041849 A041124 A048695 * A153873 A111325 A173056

Adjacent sequences: A329765 A329766 A329767 * A329769 A329770 A329771

Keyword

nonn,more

Author

Gus Wiseman, Nov 21 2019

Status

approved