A086922 Number of idempotent n X n (0,1) matrices over the reals.

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)

Links

Table of n, a(n) for n=0..8.

Crossrefs

Cf. A000292, A028895, A132186, A222821.

Sequence in context: A135081 A296366 A110083 * A007128 A013085 A352271

Adjacent sequences: A086919 A086920 A086921 * A086923 A086924 A086925

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