The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 A334222 Adjacent sequences:  A216950 A216951 A216952 * A216954 A216955 A216956 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Sep 25 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 13 00:27 EDT 2020. Contains 336441 sequences. (Running on oeis4.)