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A320088 Number of primitive (=aperiodic) 4-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet. 3
1, 4, 19, 79, 334, 1339, 5434, 21754, 87274, 349159, 1397734, 5590954, 22368169, 89472934, 357908119, 1431633559, 5726600854, 22906403494, 91625880229, 366503524969, 1466015148634, 5864060611159, 23456246655574, 93824986622614, 375299963333014, 1501199853398419 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1661

FORMULA

a(n) = Sum_{j=1..n} Sum_{d|j} 4^(d-1) * mu(j/d).

a(n) = A143327(n,4).

a(n) = Sum_{j=1..n} A143325(j,4).

a(n) = A143326(n,4) / 4.

G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 4*x^k). - Ilya Gutkovskiy, Dec 11 2020

MAPLE

b:= n-> add(`if`(d=n, 4^(n-1), -b(d)), d=numtheory[divisors](n)):

a:= proc(n) option remember; b(n)+`if`(n<2, 0, a(n-1)) end:

seq(a(n), n=1..30);

MATHEMATICA

nmax = 20; Rest[CoefficientList[Series[1/(1-x) * Sum[MoebiusMu[k] * x^k / (1 - 4*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

PROG

(PARI) a(n) = sum(j=1, n, sumdiv(j, d, 4^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020

CROSSREFS

Column k=4 of A143327.

Partial sums of A295505.

Cf. A008683, A143325, A143326.

Sequence in context: A037590 A037681 A156760 * A122909 A215037 A181300

Adjacent sequences:  A320085 A320086 A320087 * A320089 A320090 A320091

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 05 2018

STATUS

approved

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Last modified October 24 16:24 EDT 2021. Contains 348233 sequences. (Running on oeis4.)