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A067281 Number of permutations of {1,2,3,...,n} where the elements of n are considered indistinguishable if they differ by a power of 2 (for example 3, 12 and 24 are all considered equivalent).

%I A067281 #18 Dec 11 2023 18:33:35
%S A067281 1,1,1,3,4,20,60,420,840,7560,37800,415800,1663200,21621600,151351200,
%T A067281 2270268000,7264857600,123502579200,1111523212800,21118941043200,
%U A067281 140792940288000,2956651746048000,32523169206528000,748032891750144000,4488197350500864000
%N A067281 Number of permutations of {1,2,3,...,n} where the elements of n are considered indistinguishable if they differ by a power of 2 (for example 3, 12 and 24 are all considered equivalent).
%C A067281 Alternatively, one can think of these sequences as permutation of {1,2,...,n} where the term n corresponds to the appropriate ideal in Z[1/2]. This description gives an obvious generalization to Z[1/n] or other localizations of Z.
%C A067281 The conjecture a(2n+1)=(2n+1)a(2n) is obviously true from the definition of the sequence and the fact that 2n+1 is the smallest element of its equivalence class. - Brian Rothbach (rothbach(AT)Math.Berkeley.EDU), Sep 15 2004
%C A067281 a(2n+1) = (2n+1)*a(2n). However, a(n+1)/a(n) is non-integral for n = {3, 15, 19...}.
%H A067281 Alois P. Heinz, <a href="/A067281/b067281.txt">Table of n, a(n) for n = 0..490</a> (terms n=1..250 from Sean A. Irvine)
%H A067281 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a067/A067281.java">Java program</a> (github)
%e A067281 a(6) = 20 since {1,2,3,4,5,6} becomes {1,1,3,1,5,3} which has 60 permutations.
%Y A067281 Cf. A000265.
%K A067281 easy,nonn
%O A067281 0,4
%A A067281 Brian Rothbach (rothbach(AT)math.berkeley.edu), Feb 23 2002
%E A067281 More terms from _Vladeta Jovovic_, Mar 09 2002
%E A067281 a(0)=1 prepended by _Alois P. Heinz_, Dec 11 2023