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A086922
Number of idempotent n X n (0,1) matrices over the reals.
1
1, 2, 8, 50, 452, 5682, 96608, 2185738, 65108492
OFFSET
0,2
COMMENTS
From Torlach Rush, Jun 18 2020: (Start)
Let m(n,k) be the number of idempotent n X n (0,1) matrices with k entries equal to 1. Then:
k | m(n,k)
-----|------------------------------------------------------
0 | 1
1 | n
2 | A028895(n - 1)
3 | 19 * A000292(n - 2)
4 | ((n - 3) (n - 2) (n - 1) (35 n - 124))/8
5 | ((n - 4) (n - 3) (n - 2) (n - 1) (631 n - 2675))/120
...
Conjecture: There is no closed form expression for this sequence.
(End)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 19 2003
EXTENSIONS
a(5)-a(6) from Torlach Rush, Jun 17 2020
a(7)-a(8) from A222821 added by Giovanni Resta, Jun 23 2020
STATUS
approved