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Revision History for A008653 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Theta series of direct sum of 2 copies of hexagonal lattice.
(history; published version)
#35 by Peter Luschny at Sun Jan 21 02:20:12 EST 2024
STATUS

reviewed

approved

#34 by Joerg Arndt at Sun Jan 21 01:18:41 EST 2024
STATUS

proposed

reviewed

#33 by Amiram Eldar at Sun Jan 21 01:08:00 EST 2024
STATUS

editing

proposed

#32 by Amiram Eldar at Sun Jan 21 00:16:34 EST 2024
CROSSREFS
#31 by Amiram Eldar at Sun Jan 21 00:15:39 EST 2024
REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", , Springer-Verlag, 1999, p. 110.

#30 by Amiram Eldar at Sun Jan 21 00:14:37 EST 2024
COMMENTS

Convolution square of A004016.

REFERENCES

B. Bruce C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, 1991, see p. 460, Entry 3(i).

LINKS

Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>.

M. Masanobu Kaneko and Y. Yuichi Sakai, <a href="http://arxiv.org/abs/1201.1685">The Ramanujan-Serre Differential Operators and certain Elliptic Curves</a>, arXiv:1201.1685 [math.NT], 2012.

G. Gabriele Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>.

FORMULA

Convolution square of A004016Sum_{k=1..n} a(k) ~ c * n^2, where c = 2*Pi^2/3. - _Amiram Eldar_, Jan 21 2024

STATUS

approved

editing

#29 by Charles R Greathouse IV at Thu Sep 08 08:44:36 EDT 2022
PROG

(MAGMAMagma) Basis( ModularForms( Gamma0(3), 2), 70)[1]; /* Michael Somos, Jun 12 2014 */

Discussion
Thu Sep 08
08:44
OEIS Server: https://oeis.org/edit/global/2944
#28 by N. J. A. Sloane at Sun Feb 14 01:48:51 EST 2021
STATUS

editing

approved

#27 by N. J. A. Sloane at Sun Feb 14 01:48:49 EST 2021
REFERENCES

Masao Koike, Modular forms on non-compact arithmetic triangle groups, preprint.

LINKS

Masao Koike, <a href="https://oeis.org/A004016/a004016.pdf">Modular forms on non-compact arithmetic triangle groups</a>, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. I wrote 2005 on the first page but the internal evidence suggests 1997.]

STATUS

approved

editing

#26 by Alois P. Heinz at Sun Dec 10 08:03:53 EST 2017
STATUS

proposed

approved