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%I #22 Jun 25 2020 05:27:45
%S 1,2,8,50,452,5682,96608,2185738,65108492
%N Number of idempotent n X n (0,1) matrices over the reals.
%C From _Torlach Rush_, Jun 18 2020: (Start)
%C Let m(n,k) be the number of idempotent n X n (0,1) matrices with k entries equal to 1. Then:
%C k | m(n,k)
%C -----|------------------------------------------------------
%C 0 | 1
%C 1 | n
%C 2 | A028895(n - 1)
%C 3 | 19 * A000292(n - 2)
%C 4 | ((n - 3) (n - 2) (n - 1) (35 n - 124))/8
%C 5 | ((n - 4) (n - 3) (n - 2) (n - 1) (631 n - 2675))/120
%C ...
%C Conjecture: There is no closed form expression for this sequence.
%C (End)
%Y Cf. A000292, A028895, A132186, A222821.
%K nonn,more
%O 0,2
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 19 2003
%E a(5)-a(6) from _Torlach Rush_, Jun 17 2020
%E a(7)-a(8) from A222821 added by _Giovanni Resta_, Jun 23 2020
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