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A308465 Number of prefix normal palindromes of length n. 0
2, 2, 3, 3, 5, 4, 8, 7, 12, 11, 21, 18, 36, 31, 57, 55, 104, 91, 182, 166, 308, 292, 562, 512, 1009, 928, 1755, 1697, 3247, 2972, 5906, 5555, 10506, 10099, 19542, 18280, 36002, 33895, 64958, 63045, 121887, 114032, 226065, 215377, 412749, 399334, 778196, 735941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..48.

Pamela Fleischmann, On Special k-Spectra, k-Locality, and Collapsing Prefix Normal Words, Ph.D. Dissertation, Kiel University (Germany, 2021).

Pamela Fleischmann, Mitja Kulczynski, and Dirk Nowotka, On Collapsing Prefix Normal Words, arXiv:1905.11847 [cs.FL], 2019.

Pamela Fleischmann, Mitja Kulczynski, Dirk Nowotka, and Danny Bøgsted Poulsen, On Collapsing Prefix Normal Words, Language and Automata Theory and Applications (LATA 2020) LNCS Vol. 12038, Springer, Cham, 412-424.

PROG

(Python)

from itertools import product

def is_prefix_normal(w):

  for k in range(1, len(w)+1):

    weight0 = w[:k].count("1")

    for j in range(1, len(w)-k+1):

      weightj = w[j:j+k].count("1")

      if weightj > weight0: return False

  return True

def bin_pals(digits):

  midrange = [[""], ["0", "1"]]

  for p in product("01", repeat=digits//2):

    left = "".join(p)

    for middle in midrange[digits%2]:

      yield left+middle+left[::-1]

def a(n):

  return sum(is_prefix_normal(w) for w in bin_pals(n))

print([a(n) for n in range(1, 31)]) # Michael S. Branicky, Dec 19 2020

CROSSREFS

Cf. A016116 (numbers of binary palindromes), A194850 (number of prefix normal words)

Sequence in context: A275234 A097366 A139807 * A276119 A167755 A259788

Adjacent sequences:  A308462 A308463 A308464 * A308466 A308467 A308468

KEYWORD

nonn

AUTHOR

Michel Marcus, May 29 2019

EXTENSIONS

a(31)-a(48) from Michael S. Branicky, Dec 19 2020

STATUS

approved

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Last modified January 26 23:54 EST 2022. Contains 350601 sequences. (Running on oeis4.)