The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A350520 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A350520

The number of degree-n^2 polynomials over Z/2Z that can be written as f(f(x)) where f is a polynomial.
(history; published version)

#24 by N. J. A. Sloane at Fri Jan 14 07:35:58 EST 2022

STATUS

reviewed

approved

#23 by Michel Marcus at Fri Jan 14 03:42:29 EST 2022

STATUS

proposed

reviewed

#22 by Amiram Eldar at Fri Jan 14 03:15:07 EST 2022

STATUS

editing

proposed

#21 by Amiram Eldar at Fri Jan 14 03:15:01 EST 2022

CROSSREFS

Cf. A033991, A156212, A156232.

STATUS

proposed

editing

#20 by Martin Ehrenstein at Fri Jan 14 03:00:44 EST 2022

STATUS

editing

proposed

#19 by Martin Ehrenstein at Fri Jan 14 02:31:14 EST 2022

DATA

1, 1, 3, 8, 14, 32, 60, 128, 248, 512, 1008, 2048, 4064, 8192, 16320, 32768, 65408, 131072, 261888, 524288, 1048064, 2097152, 4193280, 8388608, 16775168, 33554432, 67104768, 134217728, 268427264

OFFSET

1,2

0,3

FORMULA

a(2n) = A033991(2^(n-1)) = 4^n - 2^(n-1) for n >= 1;

EXTENSIONS

a(0) prepended and a(11)-a(28) from Martin Ehrenstein, Jan 14 2022

STATUS

approved

editing

#18 by N. J. A. Sloane at Tue Jan 11 21:38:27 EST 2022

STATUS

proposed

approved

#17 by Jon E. Schoenfield at Tue Jan 11 21:24:17 EST 2022

STATUS

editing

proposed

#16 by Jon E. Schoenfield at Tue Jan 11 21:24:11 EST 2022

FORMULA

a(2n) = A033991(2^(n-1)) = 4^n - 2^(n-1).;

a(2n+1) = 2^(2n+1) for n >= 1.

EXAMPLE

x^4 = f(f(x)) when f(x) = x^2 or f(x) = x^2 + 1,

x^4 + x = f(f(x)) when f(x) = x^2 + x, and

x^4 + x + 1 = f(f(x)) when f(x) = x^2 + x + 1.

STATUS

approved

editing

Discussion

Tue Jan 11

21:24

Jon E. Schoenfield: Is this okay?

#15 by Jon E. Schoenfield at Tue Jan 11 21:23:31 EST 2022

EXAMPLE

x^4 = f(f(x)) when f(x) = x^2 or f(x) = x^2 + 1,

x^4 + x = f(f(x)) when f(x) = x^2 + x, and

x^4 + x + 1 = f(f(x)) when f(x) = x^2 + x + 1.

STATUS

editing

approved