The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A006527 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A006527

a(n) = (n^3 + 2*n)/3.
(history; published version)

#136 by N. J. A. Sloane at Fri Sep 01 04:20:52 EDT 2023

STATUS

proposed

approved

#135 by Michel Marcus at Thu Aug 31 17:11:28 EDT 2023

STATUS

editing

proposed

#134 by Michel Marcus at Thu Aug 31 17:11:24 EDT 2023

LINKS

Richard A. Brualdi, and Geir Dahl, <a href="https://arxiv.org/abs/1704.07752">Alternating Sign Matrices and Hypermatrices, and a Generalization of Latin Square</a>, arXiv:1704.07752 [math.CO], 2017. See p. 8.

STATUS

proposed

editing

#133 by Stefano Spezia at Thu Aug 31 15:01:55 EDT 2023

STATUS

editing

proposed

#132 by Stefano Spezia at Thu Aug 31 14:12:01 EDT 2023

FORMULA

Sum_{n>=0} 1/a(n) = 3*(2*gamma + polygamma(0, 1-i*sqrt(2)) + polygamma(0, 1+i*sqrt(2))/4 = 1.45245201414472469745354677573358867... where i denotes the imaginary unit. - Stefano Spezia, Aug 31 2023

#131 by Stefano Spezia at Thu Aug 31 13:44:27 EDT 2023

CROSSREFS

Cf. A002264, A005843, A054602, A059100, A135184, A158822, A177342.

#130 by Stefano Spezia at Thu Aug 31 13:40:16 EDT 2023

DATA

0, 1, 4, 11, 24, 45, 76, 119, 176, 249, 340, 451, 584, 741, 924, 1135, 1376, 1649, 1956, 2299, 2680, 3101, 3564, 4071, 4624, 5225, 5876, 6579, 7336, 8149, 9020, 9951, 10944, 12001, 13124, 14315, 15576, 16909, 18316, 19799, 21360, 23001, 24724, 26531, 28424, 30405

#129 by Stefano Spezia at Thu Aug 31 13:38:12 EDT 2023

FORMULA

Sum_{n>=0} 1/a(n) = 3*(2*gamma + polygamma(0, 1-i*sqrt(2)) + polygamma(0, 1+i*sqrt(2))/4 = 1.45245201414472469745354677573358867... where i denotes the imaginary unit. - Stefano Spezia, Aug 31 2023

STATUS

approved

editing

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

PROG

(MAGMAMagma) [(n^3 + 2*n)/3: n in [0..50]]; // Vincenzo Librandi, May 15 2011

Discussion

Thu Sep 08

08:44

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

#127 by Charles R Greathouse IV at Wed Apr 13 13:25:18 EDT 2022

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.

Discussion

Wed Apr 13

13:25

OEIS Server: https://oeis.org/edit/global/2938