The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000447 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A000447

a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3.
(history; published version)

#176 by Peter Luschny at Sun Feb 12 13:30:53 EST 2023

STATUS

proposed

approved

#175 by Michel Marcus at Sun Feb 12 13:15:55 EST 2023

STATUS

editing

proposed

#174 by Michel Marcus at Sun Feb 12 13:15:49 EST 2023

COMMENTS

Also the number of cubes in the n-th Hauy Haüy square pyramid. - Eric W. Weisstein, Sep 27 2017

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HauyConstruction.html">Hauy Haüy Construction</a>.

STATUS

approved

editing

#173 by Alois P. Heinz at Sun Feb 12 12:30:34 EST 2023

STATUS

proposed

approved

#172 by Chai Wah Wu at Sun Feb 12 12:22:19 EST 2023

STATUS

editing

proposed

#171 by Chai Wah Wu at Sun Feb 12 12:22:09 EST 2023

PROG

(Python)

def A000447(n): return n*((n**2<<2)-1)//3 # Chai Wah Wu, Feb 12 2023

STATUS

approved

editing

#170 by Charles R Greathouse IV at Thu Sep 08 08:44:28 EDT 2022

PROG

(MAGMAMagma) [n*(4*n^2-1)/3: n in [0..50]]; // Vincenzo Librandi, Jan 12 2016

Discussion

Thu Sep 08

08:44

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

#169 by N. J. A. Sloane at Tue Jan 04 05:15:59 EST 2022

STATUS

proposed

approved

#168 by Michel Marcus at Tue Jan 04 03:22:30 EST 2022

STATUS

editing

proposed

#167 by Michel Marcus at Tue Jan 04 03:22:26 EST 2022

LINKS

Milan Janjic, <a href="httphttps://wwwpmf.pmfblunibl.org/janjicwp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>.

Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992, ; arXiv:0911.4975 [math.NT], 2009.

STATUS

proposed

editing