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A295863 Number of ordered pairs of length-n mutually overlapping binary strings. 1
2, 6, 30, 130, 536, 2174, 8746, 35070, 140438, 562008, 2248460, 8994530, 35979160, 143917970, 575673270, 2302692898, 9210765608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A pair of strings (u,v) is mutually overlapping if some nonempty suffix of u is a prefix of v, and vice versa, such as (00101010,10110001).

All terms are even. - Michael S. Branicky, Dec 06 2020

LINKS

Table of n, a(n) for n=1..17.

PROG

(Python)

from itertools import product

def overlapping(u, v):

    for i in range(1, 1+min(len(u), len(v))):

        if v[:i]==u[-i:]: return True

    return False

def a(n):

    out = 0

    for u in product("01", repeat=n-1):

        u = ("0", ) + u

        for v in product("01", repeat=n):

            if overlapping(u, v) and overlapping(v, u): out += 1

    return 2*out # by symmetry

print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Dec 06 2020

CROSSREFS

Cf. A296600.

Sequence in context: A065563 A035105 A073969 * A224530 A120950 A055695

Adjacent sequences:  A295860 A295861 A295862 * A295864 A295865 A295866

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Feb 13 2018

EXTENSIONS

a(14)-a(17) from Michael S. Branicky, Dec 06 2020

STATUS

approved

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Last modified May 24 11:04 EDT 2022. Contains 354033 sequences. (Running on oeis4.)