cp's OEIS Frontend

A332800 Number of permutations sigma of [n] such that (sigma(k) mod sigma(k+1)) <= (sigma(k+1) mod sigma(k+2)) for 1 <= k <= n - 2.

%I A332800 #52 Mar 15 2020 05:53:32
%S A332800 1,1,2,4,9,21,44,109,241,530,1176,3180,6456,14835,34672,81877,179434,
%T A332800 479275,977224,2503363,5339049,11207391,28379591,82473713,166689486,
%U A332800 370775384,877910547,2150475950,4608590865,12146671367,24620749285,64137229920,143062854926
%N A332800 Number of permutations sigma of [n] such that (sigma(k) mod sigma(k+1)) <= (sigma(k+1) mod sigma(k+2)) for 1 <= k <= n - 2.
%C A332800 Conjecture: Number of permutations sigma such that (sigma(k) mod sigma(k+1)) < (sigma(k+1) mod sigma(k+2)) for 1 <= k <= n - 2 is equal to A022825(n). This is true for n <= 19.
%e A332800 b(n) = sigma(n) mod sigma(n+1).
%e A332800 In case of n = 3.
%e A332800     |           | b(1),b(2)
%e A332800 ----+-----------+----------
%e A332800   1 | [1, 2, 3] | [1, 2] *
%e A332800   2 | [1, 3, 2] | [1, 1]
%e A332800   3 | [2, 1, 3] | [0, 1] *
%e A332800   4 | [3, 1, 2] | [0, 1] *
%e A332800 In case of n = 4.
%e A332800     |              | b(1),b(2),b(3)
%e A332800 ----+--------------+---------------
%e A332800   1 | [1, 2, 3, 4] | [1, 2, 3] *
%e A332800   2 | [1, 3, 2, 4] | [1, 1, 2]
%e A332800   3 | [1, 4, 3, 2] | [1, 1, 1]
%e A332800   4 | [2, 1, 3, 4] | [0, 1, 3] *
%e A332800   5 | [2, 1, 4, 3] | [0, 1, 1]
%e A332800   6 | [3, 1, 2, 4] | [0, 1, 2] *
%e A332800   7 | [4, 1, 2, 3] | [0, 1, 2] *
%e A332800   8 | [4, 1, 3, 2] | [0, 1, 1]
%e A332800   9 | [4, 2, 1, 3] | [0, 0, 1]
%e A332800 * (strongly increasing)
%Y A332800 Cf. A022825.
%K A332800 nonn
%O A332800 0,3
%A A332800 _Seiichi Manyama_, Feb 27 2020
%E A332800 a(17)-a(20) from _Alois P. Heinz_, Feb 27 2020
%E A332800 a(21)-a(22) from _Giovanni Resta_, Mar 03 2020
%E A332800 a(23)-a(31) from _Bert Dobbelaere_, Mar 12 2020
%E A332800 a(32) from _Bert Dobbelaere_, Mar 15 2020