The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A275345

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A275345

Characteristic polynomials of a square matrix based on A051731 where A051731(1,N)=1 and A051731(N,N)=0 and where N=size of matrix, analogous to the Redheffer matrix.
(history; published version)

#41 by N. J. A. Sloane at Sat Apr 10 22:32:53 EDT 2021

STATUS

proposed

approved

#40 by Jon E. Schoenfield at Sat Apr 10 13:23:45 EDT 2021

STATUS

editing

proposed

Discussion

Sat Apr 10

13:25

Jon E. Schoenfield: Oops!  I'm sorry, I didn't see that this was reviewed (or maybe it hadn't yet been reviewed when I started making edits)…  :-(

13:30

Michel Marcus: don't worry

#39 by Jon E. Schoenfield at Sat Apr 10 13:23:41 EDT 2021

COMMENTS

b(N=1..Infinityinfinity)

= 1.00000, 1.61803, 1.61803, 2.00000, 1.61803, 2.20557, 1.61803, 2.32472, 2.00000, 2.20557, 1.61803, 2.67170, 1.61803, 2.20557, 2.20557, 2.61803, 1.61803, 2.67170, 1.61803, 2.67170, 2.20557, 2.20557, 1.61803, 3.08032, 2.00000, 2.20557, 2.32472, 2.67170, 1.61803, 2.93796, 1.61803, 2.89055, 2.20557, 2.20557, 2.20557, 3.21878, 1.61803, 2.20557, 2.20557, 3.08032, 1.61803, 2.93796, 1.61803, 2.67170, 2.67170, 2.20557, 1.61803, 3.45341, 2.00000, 2.67170, 2.20557, 2.67170, 1.61803, 3.08032, 2.20557, 3.08032, 2.20557, 2.20557, 1.61803, 3.53392, 1.61803, 2.20557, 2.67170, ...

It then appears that for n = 1,2,3,4,5,...Infinity ,infinity we have the table:

Row sums of coefficients start: 0, -1, 0, 0, 0, 0, 0, 0, 0, ...

EXAMPLE

{ 1},

{ 1, -1},

{-1, -1, 1},

{-1, 0, 2, -1},

{ 0, 0, 2, -3, 1},

{-1, 2, 1, -5, 4, -1},

{ 1, -3, 5, -8, 9, -5, 1},

{-1, 4, -4, -5, 15, -14, 6, -1},

{ 0, -1, 6, -17, 29, -31, 20, -7, 1},

{ 0, 0, 2, -13, 36, -55, 50, -27, 8, -1},

{ 1, -7, 23, -50, 84, -112, 112, -78, 35, -9, 1}

STATUS

reviewed

editing

#38 by Andrew Howroyd at Sat Apr 10 13:17:05 EDT 2021

STATUS

proposed

reviewed

#37 by Michel Marcus at Sat Apr 10 12:39:02 EDT 2021

STATUS

editing

proposed

#36 by Michel Marcus at Sat Apr 10 12:38:57 EDT 2021

LINKS

OeisWiki, OEIS Wiki, <a href="http://oeis.org/wiki/Prime_signatures">Prime signatures</a>

STATUS

approved

editing

#35 by N. J. A. Sloane at Sat Sep 30 11:29:51 EDT 2017

STATUS

proposed

approved

#34 by Michel Marcus at Sat Sep 30 11:13:01 EDT 2017

STATUS

editing

proposed

#33 by Michel Marcus at Sat Sep 30 11:12:01 EDT 2017

CROSSREFS

Cf. A025487. - Mats Granvik, Sep 30 2017

#32 by Michel Marcus at Sat Sep 30 11:11:44 EDT 2017

LINKS

<a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Pri#prime_signature">Index to sequences related to prime signature</a>

STATUS

proposed

editing