The On-Line Encyclopedia of Integer Sequences (OEIS)

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A204124

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) = gcd(2^(i-1), 2^(j-1)) (A144464).
(history; published version)

#15 by Alois P. Heinz at Mon Feb 13 03:05:31 EST 2023

STATUS

reviewed

approved

#14 by Joerg Arndt at Mon Feb 13 02:33:05 EST 2023

STATUS

proposed

reviewed

#13 by Michel Marcus at Mon Feb 13 02:15:42 EST 2023

STATUS

editing

proposed

#12 by Michel Marcus at Mon Feb 13 02:15:35 EST 2023

KEYWORD

tabl,tabf,sign

STATUS

approved

editing

Discussion

Mon Feb 13

02:15

Michel Marcus: tabf: see example

#11 by Joerg Arndt at Fri Aug 02 04:13:09 EDT 2019

STATUS

reviewed

approved

#10 by Joerg Arndt at Fri Aug 02 03:50:13 EDT 2019

STATUS

proposed

reviewed

#9 by Jon E. Schoenfield at Fri Aug 02 03:47:26 EDT 2019

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Fri Aug 02 03:47:24 EDT 2019

MATHEMATICA

TableForm[m[8]] (* 8x8 8 X 8 principal submatrix *)

#7 by Jon E. Schoenfield at Fri Aug 02 03:47:03 EDT 2019

NAME

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) =GCD gcd(2^(i-1), 2^(j-1)) (A144464).

EXAMPLE

1..., -1;

-3..., -2...., 1;

-1...., 11..., 3...., -1;

6..., -6..., -29..., -4..., 1;

STATUS

approved

editing

#6 by Charles R Greathouse IV at Thu Jul 12 00:39:58 EDT 2012

NAME

Array: row n shows the coefficients of the characteristic polynomial of the nth n-th principal submatrix of f(i,j)=GCD(2^(i-1),2^(j-1)) (A144464).

COMMENTS

Let p(n)=p(n,x) be the characteristic polynomial of the nth n-th principal submatrix. The zeros of p(n) are real, and they interlace the zeros of p(n+1). See A202605 and A204016 for guides to related sequences.

Discussion

Thu Jul 12

00:39

OEIS Server: https://oeis.org/edit/global/1814