

A327544


Number of lengthn 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
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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=n1):
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



