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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 (list; graph; refs; listen; history; text; internal format)
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 A277506

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

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Last modified September 23 01:32 EDT 2020. Contains 337291 sequences. (Running on oeis4.)