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A008706 Coordination sequence for 3.3.3.4.4 planar net. 27

%I

%S 1,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,

%T 110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,

%U 195,200,205,210,215,220

%N Coordination sequence for 3.3.3.4.4 planar net.

%C Also the Engel expansion of exp^(1/5); cf. A006784 for the Engel expansion definition. - _Benoit Cloitre_, Mar 03 2002

%H Vincenzo Librandi, <a href="/A008706/b008706.txt">Table of n, a(n) for n = 0..10000</a>

%H Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

%H C. Goodman-Strauss and N. J. A. Sloane, <a href="http://arxiv.org/abs/1803.08530">A Coloring Book Approach to Finding Coordination Sequences</a>, arXiv:1803.08530, March 2018.

%H Branko Grünbaum and Geoffrey C. Shephard, <a href="http://www.jstor.org/stable/2689529">Tilings by regular polygons</a>, Mathematics Magazine, 50 (1977), 227-247.

%H Reticular Chemistry Structure Resource, <a href="http://rcsr.net/layers/cem">cem</a>

%H N. J. A. Sloane, <a href="/A008576/a008576.png">The uniform planar nets and their A-numbers</a> [Annotated scanned figure from Gruenbaum and Shephard (1977)]

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

%F G.f.: (1+3*x+x^2)/(1-x)^2; a(n) = 0^n + 5n. - _Paul Barry_, Jul 21 2003

%t Join[{1}, LinearRecurrence[{2, -1}, {5, 10}, 100]] (* _Jean-François Alcover_, Dec 13 2018 *)

%o (MAGMA) [0^n+5*n: n in [0..50] ]; // _Vincenzo Librandi_, Aug 21 2011

%o (PARI) a(n)=0^n+5*n \\ _Charles R Greathouse IV_, Mar 19 2015

%Y Cf. A008587.

%Y List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706 (3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120 (3.3.3.3.6), A250122 (3.12.12).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified January 18 10:53 EST 2019. Contains 319271 sequences. (Running on oeis4.)