The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000389 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A000389

Binomial coefficients C(n,5).
(history; published version)

#249 by Peter Luschny at Sat Jun 22 07:58:22 EDT 2024

STATUS

reviewed

approved

#248 by Joerg Arndt at Sat Jun 22 04:57:43 EDT 2024

STATUS

proposed

reviewed

#247 by Peter Bala at Thu Jun 13 10:37:41 EDT 2024

STATUS

editing

proposed

#246 by Peter Bala at Wed Jun 12 12:22:14 EDT 2024

COMMENTS

For integer m and positive integer r >= 4, the polynomial a(n) + a(n + m) + a(n + 2*m) + ... + a(n + r*m) in n has its zeros on the vertical line Re(n) = (4 - r*m)/2 in the complex plane. - Peter Bala, Jun 02 2024

FORMULA

Conjecture: for integer r >= 4, the polynomial a(n) + a(n+1) + ... + a(n+r) has its zeros on the vertical line Re(n) = (4 - r)/2 in the complex plane. - Peter Bala, Jun 02 2024

#245 by Peter Bala at Sun Jun 02 07:30:11 EDT 2024

FORMULA

a(n+4) = 1*C(n,1) + 4*C(n,2) + 6*C(n,3) + 4*C(n,4) + 1*C(n,5), where the coefficient of C(n,k) is the number of unoriented pentachoron colorings using exactly k colors. (End)

(End)

Conjecture: for integer r >= 4, the polynomial a(n) + a(n+1) + ... + a(n+r) has its zeros on the vertical line Re(n) = (4 - r)/2 in the complex plane. - Peter Bala, Jun 02 2024

STATUS

approved

editing

Discussion

Sun Jun 09

08:47

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A000389 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#244 by Charles R Greathouse IV at Thu Sep 08 08:44:27 EDT 2022

PROG

(MAGMAMagma) [Binomial(n, 5): n in [0..40]]; // Vincenzo Librandi, Mar 12 2015

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#243 by Joerg Arndt at Sat Apr 23 01:34:44 EDT 2022

STATUS

reviewed

approved

#242 by Michel Marcus at Sat Apr 23 00:39:07 EDT 2022

STATUS

proposed

reviewed

#241 by Michael De Vlieger at Fri Apr 22 18:12:18 EDT 2022

STATUS

editing

proposed

#240 by Michael De Vlieger at Fri Apr 22 17:49:08 EDT 2022

LINKS

Ângela Mestre, and José Agapito, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Mestre/mestre2.html">Square Matrices Generated by Sequences of Riordan Arrays</a>, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.

Rajesh Kumar Mohapatra and Tzung-Pei Hong, <a href="https://doi.org/10.3390/math10071161">On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences</a>, Mathematics (2022) Vol. 10, No. 7, 1161.

STATUS

approved

editing