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 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES For references see A027375. LINKS 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 (* Jean-François 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

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)