The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A004126 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A004126

a(n) = n*(7*n^2 - 1)/6.
(history; published version)

#62 by Charles R Greathouse IV at Thu Sep 08 08:44:32 EDT 2022

PROG

(MAGMAMagma) [n*(7*n^2-1)/6: n in [0..50]]; // Vincenzo Librandi, May 15 2011

Discussion

Thu Sep 08

08:44

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

#61 by Bruno Berselli at Wed May 23 10:10:12 EDT 2018

STATUS

editing

approved

#60 by Bruno Berselli at Wed May 23 10:10:08 EDT 2018

FORMULA

a(n) = n^3 + Sum_{k=0..n-1} k*(k+1)/2 for n>0. Equivalently, Alternately, a(n) = A000578(n) + A000292(n-1) for n>0. - Bruno Berselli, May 23 2018

STATUS

proposed

editing

#59 by Bruno Berselli at Wed May 23 05:43:44 EDT 2018

STATUS

editing

proposed

Discussion

Wed May 23

06:55

Michel Marcus: your 1st formula also works for n=0, no ?

08:19

Bruno Berselli: Yes, but I don't like "k=0..-1". However, Michel, you are free to remove that limitation ;)

#58 by Bruno Berselli at Wed May 23 05:43:41 EDT 2018

FORMULA

a(n) = n^3 + Sum_{k=0..n-1} k*(k+1)/2 for n>0. Equivalently, a(n) = A000578(n) + A000292(n-1) for n>0. - Bruno Berselli, May 23 2018

#57 by Bruno Berselli at Wed May 23 05:41:49 EDT 2018

FORMULA

a(n) = n^3 + Sum_{k=0..n-1} k*(k+1)/2 for n>0. Equivalently, a(n) = A000578(n) + A000292(n-1). - Bruno Berselli, May 23 2018

STATUS

approved

editing

#56 by Joerg Arndt at Wed Sep 06 12:20:00 EDT 2017

STATUS

proposed

approved

#55 by Bruno Berselli at Wed Sep 06 11:23:51 EDT 2017

STATUS

editing

proposed

#54 by Bruno Berselli at Wed Sep 06 11:23:09 EDT 2017

COMMENTS

Sum of n triangular numbers starting from T(n), where T = A000217. E.g., a(4) = T(4) + T(5) + T(6) + T(7) = 10 + 15 + 21 + 28 = 74. - Amarnath Murthy, Jul 16 2004

Also as a(n) = (1/6)*(7*n^3-n), n>0: structured heptagonal diamond numbers (vertex structure 8). Cf. A100179 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers. - James A. Record (james.record(AT)gmail.com), Nov 07 2004

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).

FORMULA

a(n) = Sum_{i = n..2*n-1} A000217(i). - Bruno Berselli, Sep 06 2017

MATHEMATICA

Table[n (7n7 n^2 - 1)/6, {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)

PROG

(Maxima) A004126(n):=n*(7*n^2-1)/6$ makelist(A004126n*(7*n^2-1), /6, n, 0, 30); /* Martin Ettl, Jan 08 2013 */

STATUS

approved

editing

#53 by Ray Chandler at Tue Mar 21 09:45:11 EDT 2017

STATUS

editing

approved