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Ranks of involutions in permutation orderings A060117 and A060118.
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%I #13 Aug 17 2016 22:16:55

%S 0,1,2,4,6,7,12,16,18,20,24,25,26,28,48,49,60,66,72,76,78,90,96,98,

%T 102,108,120,121,122,124,126,127,132,136,138,140,240,241,242,244,288,

%U 289,312,316,336,338,360,361,372,378,384,385,432,450,456,468,480,484,486,498,504,508,528,546,576,582,600,602,606,612,624,626,648,660,672,678,720,721

%N Ranks of involutions in permutation orderings A060117 and A060118.

%C From _Antti Karttunen_, Aug 17 2016: (Start)

%C Intersection of A275804 and A276005. In other words, these are numbers in whose factorial base representation (A007623, see A260743) there does not exist any such pair of nonzero digits d_i and d_j in positions i and j that either (i - d_i) = j or (i - d_i) = (j - d_j) would hold. Here one-based indexing is used so that the least significant digit at right is in position 1.

%C (End)

%H Antti Karttunen, <a href="/A261220/b261220.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%o (Scheme, three variants, all requiring _Antti Karttunen_'s IntSeq-library)

%o (define A261220 (ZERO-POS 0 0 (lambda (n) (+ (A275947 n) (A276007 n)))))

%o (define A261220 (MATCHING-POS 0 0 (lambda (n) (>= 2 (A275803 n)))))

%o (define A261220 (MATCHING-POS 0 0 (lambda (n) (>= 2 (A060131 n)))))

%Y Intersection of A275804 and A276005.

%Y Same sequence shown in factorial base: A260743.

%Y Cf. A060117, A060118, A275947, A276007.

%Y Positions of zeros in A261219.

%Y Positions of 1 and 2's in A060131 and A275803.

%Y Subsequence: A060112.

%Y Cf. also A014489.

%K nonn,base

%O 0,3

%A _Antti Karttunen_, Aug 26 2015