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A327544 Number of length-n binary words whose longest repeated suffix equals the longest repeated prefix. 1
2, 4, 4, 10, 16, 28, 44, 90, 156, 270, 488, 886, 1620, 2986, 5460, 10120, 18890, 35284, 66290, 124964, 236040, 447460, 850492, 1620016, 3092652, 5915898, 11336182, 21760238, 41836338, 80549326, 155296862, 299788294, 579396418, 1121031734, 2171251698 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The longest repeated suffix of a word x is the longest suffix (possibly empty) that occurs at least twice as a contiguous block inside x, and analogously for the prefix.

LINKS

Table of n, a(n) for n=1..35.

Michael S. Branicky, Python program.

EXAMPLE

For n = 5 these binary words are 00000, 00100, 00110, 01001, 01010, 01100, 01101, 01110 and their reversals.

PROG

(Python) # see link for faster version

from itertools import product

def lrp(s): # longest repeated prefix (overlaps allowed)

  for i in range(len(s)-1, 0, -1):

    if s.find(s[:i], 1) >= 0: return s[:i]

  return ""

def a(n):

  if n == 1: return 2

  c = 0

  for p in product("01", repeat=n-1):

    b = "1" + "".join(p)

    if lrp(b) == lrp(b[::-1])[::-1]: c += 1

  return 2*c

print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Feb 05 2021

CROSSREFS

Sequence in context: A267311 A118336 A193852 * A202076 A199825 A121049

Adjacent sequences:  A327541 A327542 A327543 * A327545 A327546 A327547

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Sep 16 2019

EXTENSIONS

a(29) and beyond from Michael S. Branicky, Feb 05 2021

STATUS

approved

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Last modified January 26 18:26 EST 2022. Contains 350599 sequences. (Running on oeis4.)