

A234275


Expansion of (1+2*x+9*x^24*x^3)/(1x)^2.


22



1, 4, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432
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OFFSET

0,2


COMMENTS

Also the coordination sequence for a point of degree 4 in the tiling of the Euclidean plane by right triangles (with angles Pi/2, Pi/4, Pi/4). These triangles are fundamental regions for the Coxeter group (2,4,4). In the notation of Conway et al. 2008 this is the tiling *442. The coordination sequence for a point of degree 8 is given by A022144.  N. J. A. Sloane, Dec 28 2015
First differences of number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 899", based on the 5celled von Neumann neighborhood. Initialized with a single black (ON) cell at stage zero.  Robert Price, May 28 2016


REFERENCES

J. H. Conway, H. Burgiel and C. GoodmanStrauss, The Symmetries of Things, A K Peters, Ltd., 2008, ISBN 9781568812205. See p. 191.
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
J. Choi, N. Pippenger, Counting the Angels and Devils in Escher's Circle Limit IV, arXiv preprint arXiv:1310.1357, 2013.
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
N. J. A. Sloane, Overview of coordination sequences of Laves tilings [Fig. 2.7.1 of GrünbaumShephard 1987 with Anumbers added and in some cases the name in the RCSR database]
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to 2D 5Neighbor Cellular Automata
Index to Elementary Cellular Automata
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(n) = A022144(n), n>1.  R. J. Mathar, Jan 11 2014
From Colin Barker, Jul 10 2015: (Start)
a(n) = 8*n, n>1.
a(n) = 2*a(n1)  a(n2) for n>3.
G.f.: (4*x^39*x^22*x1) / (x1)^2.
(End)


MATHEMATICA

Join[{1, 4}, LinearRecurrence[{2, 1}, {16, 24}, 60]] (* JeanFrançois Alcover, Jan 08 2019 *)


PROG

(PARI) Vec((4*x^39*x^22*x1)/(x1)^2 + O(x^100)) \\ Colin Barker, Jul 10 2015


CROSSREFS

Cf. A022144.
For partial sums see A265056.
List of coordination sequences for Laves tilings (or duals of uniform planar nets): [3,3,3,3,3.3] = A008486; [3.3.3.3.6] = A298014, A298015, A298016; [3.3.3.4.4] = A298022, A298024; [3.3.4.3.4] = A008574, A296368; [3.6.3.6] = A298026, A298028; [3.4.6.4] = A298029, A298031, A298033; [3.12.12] = A019557, A298035; [4.4.4.4] = A008574; [4.6.12] = A298036, A298038, A298040; [4.8.8] = A022144, A234275; [6.6.6] = A008458.
Sequence in context: A237878 A065661 A100275 * A284810 A192199 A145229
Adjacent sequences: A234272 A234273 A234274 * A234276 A234277 A234278


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 24 2013


STATUS

approved



