The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A008486

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A008486

Expansion of (1 + x + x^2)/(1 - x)^2.
(history; published version)

#159 by Stefano Spezia at Sun Aug 07 15:28:21 EDT 2022

CROSSREFS

Cf. A000217, A006784, A008585, A022424, A113062.

#158 by Stefano Spezia at Sun Aug 07 15:26:28 EDT 2022

FORMULA

E.g.f.: 1 + 3*exp(x)*x. - Stefano Spezia, Aug 07 2022

PROG

(MAGMAMagma) [0^n+3*n: n in [0..90] ]; // Vincenzo Librandi, Aug 21 2011

STATUS

approved

editing

#157 by Andrew Howroyd at Tue Dec 29 13:13:19 EST 2020

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reviewed

approved

#156 by Joerg Arndt at Tue Dec 29 09:09:47 EST 2020

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proposed

reviewed

#155 by Michel Marcus at Tue Dec 29 08:52:38 EST 2020

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editing

proposed

#154 by Michel Marcus at Tue Dec 29 08:52:31 EST 2020

COMMENTS

Coordination sequence for planar net 6^3 (the graphite net, or the graphene crystal) - that is, the number of atoms at graph distance n from any fixed atom. Also for the hcb or honeycomb net. - N. J. A. Sloane, Jan 06 2013, Mar 31 2018.

LINKS

Chaim Goodman-Strauss and N. J. A. Sloane, <a href="https://doi.org/10.1107/S2053273318014481">A Coloring Book Approach to Finding Coordination Sequences</a>, Acta Cryst. A75 (2019), 121-134, also <a href="http://NeilSloane.com/doc/Cairo_final.pdf">on NJAS's home page</a>. Also <a href="http://arxiv.org/abs/1803.08530">on arXiv</a>, arXiv:1803.08530</a> [math.CO], 2018-2019.

Rostislav Grigorchuk and Cosmas Kravaris, <a href="https://arxiv.org/abs/2012.13661">On the growth of the wallpaper groups</a>, arXiv:2012.13661 [math.GR], 2020. See section 4.3 p. 20.

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).

STATUS

approved

editing

#153 by N. J. A. Sloane at Sat Apr 04 01:28:15 EDT 2020

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editing

approved

#152 by N. J. A. Sloane at Sat Apr 04 01:28:11 EDT 2020

LINKS

Tom Karzes, <a href="/A250122/a250122.html">Tiling Coordination Sequences</a>

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approved

editing

#151 by Alois P. Heinz at Fri Feb 21 11:09:24 EST 2020

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proposed

approved

#150 by Michel Marcus at Fri Feb 21 11:07:10 EST 2020

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editing

proposed