The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A358649 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A358649

Number of convergent n X n matrices over GF(2).
(history; published version)

#25 by N. J. A. Sloane at Sun Nov 27 10:50:00 EST 2022

STATUS

proposed

approved

#24 by Jon E. Schoenfield at Sat Nov 26 17:52:19 EST 2022

STATUS

editing

proposed

#23 by Jon E. Schoenfield at Sat Nov 26 17:52:17 EST 2022

FORMULA

a(n) = Sum_{k=0..n} A296548(n,k)*A053763(n-k).

STATUS

proposed

editing

#22 by Geoffrey Critzer at Sat Nov 26 17:37:12 EST 2022

STATUS

editing

proposed

#21 by Geoffrey Critzer at Sat Nov 26 17:36:32 EST 2022

COMMENTS

A matrix A over a finite field is convergent if A^j=A^(j+1) for some j>=1. Every convergent matrix converges to an idempotent matrix. Every idempotent matrix is convergent to itself. Every nilpotent matrix is convergent to the zero matrix.

CROSSREFS

Cf. A296548, A053763, A132186.

STATUS

proposed

editing

#20 by Geoffrey Critzer at Sat Nov 26 17:32:19 EST 2022

STATUS

editing

proposed

#19 by Geoffrey Critzer at Sat Nov 26 17:30:07 EST 2022

NAME

allocated for Geoffrey CritzerNumber of convergent n X n matrices over GF(2).

DATA

1, 2, 11, 205, 14137, 3755249, 3916674017, 16190352314305, 266479066904477569, 17503939768635307654913, 4593798697440979773283368449, 4819699338906053452395454422580225, 20221058158328101246044232181365184919553

OFFSET

0,2

COMMENTS

A matrix A over a finite field is convergent if A^j=A^(j+1) for some j>=1. Every convergent matrix converges to an idempotent matrix.

FORMULA

a(n) = Sum_{k=0..n}A296548(n,k)*A053763(n-k)

MATHEMATICA

nn = 12; q = 2; g[n_] := Product[q^n - q^i, {i, 0, n - 1}]; Table[Sum[g[n]/(g[k] g[n - k]) q^((n - k) (n - k - 1)), {k, 0, n}], {n, 0, nn}]

CROSSREFS

Cf. A296548, A053763.

KEYWORD

allocated

nonn

AUTHOR

Geoffrey Critzer, Nov 26 2022

STATUS

approved

editing

#18 by Geoffrey Critzer at Sat Nov 26 17:30:07 EST 2022

NAME

allocated for Geoffrey Critzer

KEYWORD

recycled

allocated

#17 by Hugo Pfoertner at Sat Nov 26 16:16:20 EST 2022

STATUS

proposed

approved

#16 by Kevin Ryde at Sat Nov 26 16:15:08 EST 2022

STATUS

editing

proposed