

A216953


Triangle read by rows: T(n,k) (n>=1, 1<=k<=n) = number of binary sequences of length n with minimal period k.


2



2, 2, 2, 2, 0, 6, 2, 2, 0, 12, 2, 0, 0, 0, 30, 2, 2, 6, 0, 0, 54, 2, 0, 0, 0, 0, 0, 126, 2, 2, 0, 12, 0, 0, 0, 240, 2, 0, 6, 0, 0, 0, 0, 0, 504, 2, 2, 0, 0, 30, 0, 0, 0, 0, 990, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2046, 2, 2, 6, 12, 0, 54, 0, 0, 0, 0, 0, 4020, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8190, 2, 2, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, 0, 16254
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OFFSET

1,1


REFERENCES

For references see A027375.


LINKS

Table of n, a(n) for n=1..105.
B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102 [math.CO], Dec 25 2012.
B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.


FORMULA

If k divides n, T(n,k) = A027375(k), otherwise 0.


EXAMPLE

Triangle begins:
2,
2, 2,
2, 0, 6,
2, 2, 0, 12,
2, 0, 0, 0, 30,
2, 2, 6, 0, 0, 54,
2, 0, 0, 0, 0, 0, 126,
2, 2, 0, 12, 0, 0, 0, 240,
2, 0, 6, 0, 0, 0, 0, 0, 504,
2, 2, 0, 0, 30, 0, 0, 0, 0, 990,
...
For n=4 the 16 sequences are:
0000, 1111, period 1,
0101, 1010, period 2,
and the rest have period 4.


MAPLE

with(numtheory): A027375:=n>add( mobius(d)*2^(n/d), d in divisors(n));
a:=proc(n, k) global A027375;
if n mod k = 0 then A027375(k) else 0; fi; end;


MATHEMATICA

a027375[n_] := DivisorSum[n, MoebiusMu[n/#]*2^#&];
T[n_, k_] := If[Divisible[n, k], a027375[k], 0];
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* JeanFrançois Alcover, Nov 26 2017 *)


CROSSREFS

Cf. A027375 (the main diagonal), A216954, A001037.
Sequence in context: A159782 A268242 A309509 * A326786 A276206 A124752
Adjacent sequences: A216950 A216951 A216952 * A216954 A216955 A216956


KEYWORD

nonn,tabl


AUTHOR

N. J. A. Sloane, Sep 25 2012


STATUS

approved



