A329768 - OEIS

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

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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