

A045690


Number of binary words of length n (beginning with 0) whose autocorrelation function is the indicator of a singleton.


11



1, 1, 2, 3, 6, 10, 20, 37, 74, 142, 284, 558, 1116, 2212, 4424, 8811, 17622, 35170, 70340, 140538, 281076, 561868, 1123736, 2246914, 4493828, 8986540, 17973080, 35943948, 71887896, 143771368, 287542736, 575076661, 1150153322, 2300289022
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OFFSET

1,3


COMMENTS

The number of binary strings sharing the same autocorrelations.
Appears to be row sums of A155092, beginning from a(2).  Mats Granvik, Jan 20 2009
The number of binary words of length n (beginning with 0) which do not start with an even palindrome (i.e. which are not of the form ss*t where s is a (nonempty) word, s* is its reverse, and t is any (possibly empty) word).  Mamuka Jibladze, Sep 30 2014


LINKS

T. D. Noe, Table of n, a(n) for n = 1..500
E. H. Rivals, Autocorrelation of Strings.
E. H. Rivals, S. Rahmann Combinatorics of Periods in Strings
E. H. Rivals, S. Rahmann, Combinatorics of Periods in Strings, Journal of Combinatorial Theory  Series A, Vol. 104(1) (2003), pp. 95113.
T. Sillke, How many words have the same autocorrelation value?


FORMULA

a(2n) = 2*a(2n1)  a(n) for n >= 1; a(2n+1) = 2*a(2n) for n >= 1.


MATHEMATICA

a[1] = 1; a[n_] := a[n] = If[EvenQ[n], 2*a[n1]  a[n/2], 2*a[n1]]; Array[a, 40] (* JeanFrançois Alcover, Jul 17 2015 *)


PROG

(PARI) a(n)=if(n<2, n>0, 2*a(n1)(1n%2)*a(n\2))


CROSSREFS

Cf. A002083, A005434. A003000 = 2*a(n) for n > 0.
Different from, but easily confused with, A007148 and A093371.
Sequence in context: A008929 A164047 A158291 * A007148 A093371 A003214
Adjacent sequences: A045687 A045688 A045689 * A045691 A045692 A045693


KEYWORD

nonn,easy,nice


AUTHOR

Torsten.Sillke(AT)unibielefeld.de


EXTENSIONS

More terms from James A. Sellers.
Additional comments from Michael Somos, Jun 09 2000


STATUS

approved



