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 A058052 Sum of the distances between the 2^n vertices in the De Bruijn Graphs on words of length n on alphabet {0,1}. 0
 2, 18, 118, 680, 3620, 18274, 88760, 418900, 1933904, 8775534, 39277136, 173843142, 762388102, 3317784992, 14344443516, 61671799608, 263865053452, 1124175400716, 4771570406736, 20185774001256, 85141101913670 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Given two words X,Y in {0,1}^N, the distance d(X,Y) is the least integer K such that there exists a word M with X=UM and Y=MV and |U|=|V|=K. Define a(N)=sum(d(X,Y); X,Y in {0,1}^N). LINKS Table of n, a(n) for n=1..21. Eric Weisstein's World of Mathematics, de Bruijn Sequence. EXAMPLE d(0,0)=0, d(0,1)=1, d(1,0)=1, d(1,1)=0, hence a(1)=0+1+1+0=2. d(00,00)=0, d(00,01)=1, d(00,10)=2, d(00,11)=2, d(01,00)=2, d(01,01)=0, d(01,10)=1, d(01,11)=1, d(10,00)=1, d(10,01)=1, d(10,10)=0, d(10,11)=2, d(11,00)=2, d(11,01)=2, d(11,10)=1, d(11,11)=0, hence a(2)=0+1+2+2+2+0+1+1+1+1+0+2+2+2+1+0=18. PROG (Python) from numba import njit @njit def d(x, y, n): for k in range(n): mask = (1 << (n-k)) - 1 if x & mask == (y >> k): return k return n @njit def a(n): s = 0 for x in range(2**(n-1)): for y in range(2**n): s += d(x, y, n) return 2*s print([a(n) for n in range(1, 15)]) # Michael S. Branicky, Feb 18 2021 CROSSREFS Cf. A166316. Sequence in context: A027433 A153338 A007798 * A119578 A052610 A052653 Adjacent sequences: A058049 A058050 A058051 * A058053 A058054 A058055 KEYWORD nonn AUTHOR Serge Burckel (burckel(AT)iml.univ-mrs.fr), Nov 19 2000 EXTENSIONS a(9)-a(21) from Michael S. Branicky, Feb 18 2021 STATUS approved

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Last modified April 23 23:26 EDT 2024. Contains 371917 sequences. (Running on oeis4.)