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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: A114328 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 May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)