The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A006528 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A006528

a(n) = (n^4 + n^2 + 2*n)/4.
(history; published version)

#72 by Michael De Vlieger at Wed Oct 11 11:26:45 EDT 2023

STATUS

reviewed

approved

#71 by Michel Marcus at Wed Oct 11 11:24:33 EDT 2023

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proposed

reviewed

#70 by Stefano Spezia at Wed Oct 11 11:09:25 EDT 2023

STATUS

editing

proposed

#69 by Stefano Spezia at Wed Oct 11 11:09:07 EDT 2023

DATA

0, 1, 6, 24, 70, 165, 336, 616, 1044, 1665, 2530, 3696, 5226, 7189, 9660, 12720, 16456, 20961, 26334, 32680, 40110, 48741, 58696, 70104, 83100, 97825, 114426, 133056, 153874, 177045, 202740, 231136, 262416, 296769, 334390, 375480, 420246, 468901, 521664, 578760

#68 by Stefano Spezia at Wed Oct 11 11:06:59 EDT 2023

COMMENTS

Also product of first and last terms in n-th row of a triangle of form: row(1)= 1; row(2)= 2,3; row(3) = 4, 5, 6, ... . - Dave Durgin, Aug 17 2012

FORMULA

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). [_- _Vincenzo Librandi_, Apr 30 2012]

From Stefano Spezia, Oct 11 2023: (Start)

O.g.f.: x*(1 + x + 4*x^2)/(1 - x)^5.

E.g.f.: exp(x)*x*(4 + 8*x + 6*x^2 + x^3)/4. (End)

STATUS

approved

editing

#67 by Charles R Greathouse IV at Thu Sep 08 08:44:35 EDT 2022

PROG

(MAGMAMagma) I:=[0, 1, 6, 24, 70]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Apr 30 2012

Discussion

Thu Sep 08

08:44

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

#66 by Alois P. Heinz at Thu Apr 15 11:07:58 EDT 2021

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reviewed

approved

#65 by Joerg Arndt at Thu Apr 15 10:52:03 EDT 2021

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proposed

reviewed

#64 by Michel Marcus at Thu Apr 15 10:49:12 EDT 2021

STATUS

editing

proposed

#63 by Michel Marcus at Thu Apr 15 10:49:05 EDT 2021

LINKS

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.

Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.

STATUS

approved

editing