

A284462


Number of lengthn binary strings s whose longest repeated suffix appears exactly twice in s.


0



2, 2, 6, 10, 22, 44, 92, 178, 362, 724, 1444, 2888, 5792, 11616, 23300, 46670, 93434, 186988, 374012, 747976, 1495656, 2990440, 5979368, 11956444, 23910164, 47819272, 95645168, 191318496, 382719072, 765644448, 1531761528, 3064550802
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OFFSET

1,1


COMMENTS

By "longest repeated suffix" we mean the longest suffix that occurs in at least one other position in the string; occurrences may overlap. Thus the longest repeated suffix of "alfalfa" is "alfa".


LINKS

Table of n, a(n) for n=1..32.


EXAMPLE

For n = 4 the exceptions are 0001 and 1110 (longest repeated suffix is empty); 0010 and 0100 (longest repeated suffix is 0, which appears three times); and 1011 and 1101 (longest repeated suffix is 1, which appears three times).


MAPLE

g:= proc(S) local m, n, t;
n:= nops(S);
for m from n1 to 1 by 1 do
t:= nops(select(j > S[1..m] = S[j..m+j1], [$2..nm+1]));
if t >= 1 then return evalb(t=1) fi;
od;
false
end proc:
f:= proc(n) add(`if`(g(convert(x, base, 2)), 2, 0), x=2^(n1)..2^n1) end proc:
f(1):= 2:
map(f, [$1..20]); # Robert Israel, Mar 27 2017


CROSSREFS

Cf. A059412, A284125.
Sequence in context: A014113 A078008 A151575 * A262278 A265639 A208900
Adjacent sequences: A284459 A284460 A284461 * A284463 A284464 A284465


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Mar 27 2017


EXTENSIONS

a(21)a(32) from Lars Blomberg, Jun 06 2017


STATUS

approved



