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A109468 a(n) is the number of permutations of (1,2,3,...,n) written in binary such that no adjacent elements share a common 1-bit. 0
1, 2, 0, 4, 2, 0, 0, 0, 8, 32, 0, 8, 0, 0, 0, 0, 0, 64, 0, 1968, 508, 0, 0, 0, 16 (list; graph; refs; listen; history; text; internal format)



In other words, if b(m) and b(m+1) are adjacent elements written in binary, then (b(m) AND b(m+1)) = 0 for 1 <= m <= n-1. (If a logical AND is applied to each pair of adjacent terms, the result is zero.)

Let 2^k be the largest power of 2 <= n. Note that element 2^k-1 can be adjacent only to 2^k. So 2^k-1 must be at the beginning or the end of the permutation while 2^k must be next to 2^k-1. The elements 2^k-1-2^i (i=1,...,k-1) can be adjacent only to 2^i, 2^k and 2^k+2^i implying that n must be >=2^k+2^(k-3) to yield a nonzero number of permutations.


Table of n, a(n) for n=1..25.


Sequence in context: A199891 A339417 A226240 * A331032 A319690 A341419

Adjacent sequences:  A109465 A109466 A109467 * A109469 A109470 A109471




N. J. A. Sloane, based on a suggestion from Leroy Quet, Aug 21 2005


More terms from Max Alekseyev, Aug 28 2005



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Last modified April 12 01:36 EDT 2021. Contains 342912 sequences. (Running on oeis4.)