The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A281910

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A281910

Minimum possible absolute value over all coefficients of p(x)/(1-x)^n, where p is a power series with +-1 coefficients.
(history; published version)

#12 by N. J. A. Sloane at Thu Feb 02 08:57:51 EST 2017

STATUS

editing

approved

#11 by N. J. A. Sloane at Thu Feb 02 08:57:16 EST 2017

DATA

1, 1, 1, 2, 8, 40, 268, 2124

COMMENTS

The value of It is known that a(7) >= 2124 , and that is not known with complete certaintyconjectured to be the true value.

STATUS

reviewed

editing

Discussion

Thu Feb 02

08:57

N. J. A. Sloane: I took the more conservative route

#10 by Robert Israel at Thu Feb 02 03:01:33 EST 2017

STATUS

proposed

reviewed

Discussion

Thu Feb 02

03:03

Robert Israel: How uncertain is a(7) = 2124?  It's better to leave it out of the Data section rather than publish a possibly incorrect value.

05:23

Jeffrey Shallit: It is very certain, in my opinion.

08:01

Jeffrey Shallit: If you prefer, you can delete a(7) and just add a comment that it is known that a(7) >= 2124. I can prove that.

#9 by Joerg Arndt at Thu Feb 02 02:28:30 EST 2017

STATUS

editing

proposed

#8 by Joerg Arndt at Thu Feb 02 02:28:20 EST 2017

KEYWORD

nonn,hard,more,changed

STATUS

proposed

editing

#7 by Michel Marcus at Thu Feb 02 00:15:08 EST 2017

STATUS

editing

proposed

#6 by Michel Marcus at Thu Feb 02 00:15:04 EST 2017

KEYWORD

nonn,more,changed

STATUS

proposed

editing

#5 by Wesley Ivan Hurt at Wed Feb 01 21:27:17 EST 2017

STATUS

editing

proposed

#4 by Wesley Ivan Hurt at Wed Feb 01 21:27:02 EST 2017

EXAMPLE

For n = 3 consider p(x) = (x+1)(x-1)^2/(x^4+1). Considered as a power series , this has coefficients +- 1 only. Then p(x)/(1-x)^3 has coefficients bounded by 2 in absolute value.

STATUS

proposed

editing

#3 by Jeffrey Shallit at Wed Feb 01 18:47:38 EST 2017

STATUS

editing

proposed