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A296975 Number of aperiodic normal sequences of length n. 9
1, 2, 12, 72, 540, 4668, 47292, 545760, 7087248, 102247020, 1622632572, 28091562840, 526858348380, 10641342923148, 230283190977300, 5315654681435520, 130370767029135900, 3385534663249753392, 92801587319328411132, 2677687796244281955480, 81124824998504073834516 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A finite sequence is normal if it spans an initial interval of positive integers. It is aperiodic if every cyclic rotation is different.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

FORMULA

a(n) = n * A060223(n) = Sum_{d|n} mu(d) * A000670(n/d).

EXAMPLE

The a(3) = 12 aperiodic normal sequences are 112, 121, 122, 123, 132, 211, 212, 213, 221, 231, 312, 321.

The 15 non-aperiodic normal sequences of length 6 are: 111111, 112112, 121121, 121212, 122122, 123123, 132132, 211211, 212121, 212212, 213213, 221221, 231231, 312312, 321321.

MATHEMATICA

Table[DivisorSum[n, MoebiusMu[n/#]*Sum[k!*StirlingS2[#, k], {k, #}]&], {n, 25}]

PROG

(PARI) \\ here b(n) is A000670.

b(n)={polcoef(serlaplace(1/(2-exp(x+O(x*x^n)))), n)}

a(n)={sumdiv(n, d, moebius(d)*b(n/d))} \\ Andrew Howroyd, Aug 29 2018

CROSSREFS

Cf. A000670, A000740, A001037, A019536, A027375, A060223, A095684, A185700, A296976, A296977, A296978.

Sequence in context: A052556 A052833 A277490 * A144086 A348767 A335786

Adjacent sequences:  A296972 A296973 A296974 * A296976 A296977 A296978

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 22 2017

STATUS

approved

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Last modified May 29 07:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)