A050183 T(2n+5,n), array T as in A051168; a count of Lyndon words.

0, 1, 4, 15, 55, 200, 728, 2652, 9690, 35530, 130750, 482885, 1789515, 6653325, 24812400, 92798375, 347993910, 1308233790, 4929576600, 18615637950, 70441574000, 267058714626, 1014283603024, 3858687620200, 14702930414900

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Index entries for sequences related to Lyndon words

Formula

From Petros Hadjicostas, Dec 03 2017: (Start)

a(n) = (1/(2*n+5))*Sum_{d|gcd(n,5)} mu(d)*binomial((2*n+5)/d, n/d). (This is a special case of A. Howroyd's formula for double array A051168.)

a(n) = (1/(2*n+5))*(binomial(2*n+5, n) - binomial((2*n/5)+1, n/5)) if 5|n; = (1/(2*n+5))*binomial(2*n+5, n) otherwise.

(End)

Maple

A050183 := proc(n)
    binomial(2*n+5, n) ;
    if modp(n, 5) = 0 then
        %-binomial(2*n/5+1, n/5) ;
    end if;
    %/(2*n+5) ;
end proc:
seq(A050183(n), n=0..40) ; # R. J. Mathar, Oct 28 2021

Prog

(PARI) a(n) = (1/(2*n+5))*sumdiv(gcd(n, 5), d, moebius(d)*binomial((2*n+5)/d, n/d)); \\ Michel Marcus, Dec 05 2017

Crossrefs

A diagonal of the square array described in A051168.

Sequence in context: A220948 A026013 A371820 * A094375 A047018 A064813

Adjacent sequences: A050180 A050181 A050182 * A050184 A050185 A050186

Keyword

nonn

Author

Clark Kimberling

Status

approved