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A249179 First row of spectral array W(3^(1/3)). 0
1, 3, 4, 9, 12, 29, 41, 94, 135, 306, 441, 997, 1437, 3251, 4688, 10602, 15290, 34574, 49864, 112751, 162615, 367699, 530313, 1199127, 1729440, 3910553, 5639993, 12752965 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

3^(1/3) = 1.442249570307408382321638310780109588391869253499350577546416...

The sequence is generated from the Beatty sequence (A059539) and from the complement of the Beatty sequence (A059540) for 3^(1/3).

LINKS

Table of n, a(n) for n=1..28.

A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.

PROG

(PARI)

\\ Row i of the generalized Wythoff array W(h),

\\   where h is an irrational number between 1 and 2,

\\   and m is the number of terms in the vectors b and c.

row(h, i, m) = {

  if(h<=1 || h>=2, print("Invalid value for h"); return);

  my(

    b=vector(m, n, floor(n*h)),       \\ Beatty sequence for h

    c=vector(m, n, floor(n*h/(h-1))), \\ Complement of b

    w=[b[b[i]], c[b[i]]],

    j=3

  );

  while(1,

    if(j%2==1,

      if(w[j-1]<=#b, w=concat(w, b[w[j-1]]), return(w))

    ,

      if(w[j-2]<=#c, w=concat(w, c[w[j-2]]), return(w))

    );

    j++

  )

}

allocatemem(10^9)

default(realprecision, 100)

row(3^(1/3), 1, 10^7)

CROSSREFS

Cf. A059539, A059540.

Sequence in context: A034421 A211221 A029448 * A103014 A116552 A339996

Adjacent sequences:  A249176 A249177 A249178 * A249180 A249181 A249182

KEYWORD

nonn,more

AUTHOR

Colin Barker, Dec 03 2014

STATUS

approved

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Last modified January 16 18:07 EST 2022. Contains 350376 sequences. (Running on oeis4.)