A397135 - OEIS

A397135

Number of words of length n in S, such that S is a set containing the word ab and if a word w of the form xy is in S then w* of the form x(k^r)y is in S where k^r is the reversal of some factor k of w with |k| > 1.

1, 0, 3, 0, 19, 22, 127, 264, 734, 1674, 3640, 7726, 15872, 32222, 64961, 130442, 261475, 523570, 1047815, 2096346, 4193451, 8387708, 16776269, 33553438, 67107823, 134216640

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

COMMENTS

Here xy is some factorization of the word w into potentially empty factors x and y.

LINKS

Table of n, a(n) for n=2..27.

John Tyler Rascoe, Python code.

EXAMPLE

a(2) = 1: ab.

a(4) = 3: abab, abba, baab.

a(6) = 19: babaab, bbaaab, baabab, baabba, abbaab, baaabb, aabaab, baaaab, baabaa, ababab, ababba, aabbab, abaabb, abbaba, abbbaa, aabbba, bbabba, abbbba, abbabb.

PROG

(Python) # see links

(Python)

from itertools import count, islice

def agen(): # generator of terms

S = {2: {"ab"}}

yield 1

for n in count(3):

S[n] = set()

for i in range((n+1)//2, n-1):

for w in S[i]:

for j in range(len(w)+1):

x, y = w[:j], w[j:]

for m in range(2*i-n+1):

k = w[m:m+n-i]

S[n].add(x+k[::-1]+y)

yield len(S[n])

print(list(islice(agen(), 15))) # Michael S. Branicky, Aug 02 2026

CROSSREFS

Cf. A000079, A006697, A116456, A183135.

Sequence in context: A151814 A187804 A281554 * A320104 A102840 A009353

Adjacent sequences: A397132 A397133 A397134 * A397136 A397137 A397138

KEYWORD

nonn,more

AUTHOR

John Tyler Rascoe, Jul 20 2026

EXTENSIONS

a(19)-a(22) from Sean A. Irvine, Jul 25 2026

a(23)-a(27) from Michael S. Branicky, Aug 02 2026

STATUS

approved