A179674 Number of binary sequences of length n having a conjugate at Hamming distance 2.

0, 2, 6, 12, 30, 54, 98, 160, 234, 400, 462, 864, 806, 1722, 1530, 3328, 1938, 7290, 2774, 13360, 6090, 26422, 5106, 60096, 7900, 113256, 21600, 240240, 10614, 535980, 13082, 1065984, 82962, 2244340, 34650, 4894560, 22718, 9984462, 345930, 21050240, 31242, 44773848, 36206

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Jon Maiga, Computer-generated formulas for A179674, Sequence Machine.

Jeffrey Shallit, Hamming distance for conjugates, Discrete Mathematics 309(12): 4197-4199 (2009).

Formula

a(n) = n * A226893(n) [uncovered by sequencedb.net]. - Falk Hüffner, Aug 15 2021

Example

For n = 3 the a(3) = 6 solutions are all 8 strings except 000, 111.

Prog

(Python)
from itertools import product
def h(w, x): return sum(1 for wi, xi in zip(w, x) if wi != xi)
def ok(w):
    return any(h(w, w[s:]+w[:s]) == 2 for s in range(1, len(w)))
def a(n):
    return 2*sum(1 for p in product("01", repeat=n-1) if ok("0"+"".join(p)))
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Mar 14 2022

Crossrefs

Cf. A179677, A226893.

Sequence in context: A081375 A024701 A224532 * A038199 A056267 A348412

Adjacent sequences: A179671 A179672 A179673 * A179675 A179676 A179677

Keyword

nonn

Author

Jeffrey Shallit, Jan 09 2011

Extensions

a(18)-a(40) from Falk Hüffner, Jul 08 2018

a(41)-a(43) from Falk Hüffner, Aug 15 2021

Status

approved