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A304960 Number of business cards required to build an origami level n Mosely snowflake sponge.

%I A304960 #7 Jun 10 2018 22:34:38
%S A304960 12,168,2784,48912,874416,15709488,282620784,5086424112,91551884016,
%T A304960 1647915162288,29662379171184,533922356331312,9610600070213616,
%U A304960 172990789545095088,3113834153217961584,56049014464954558512,1008882258904338303216,18159880652953870707888
%N A304960 Number of business cards required to build an origami level n Mosely snowflake sponge.
%D A304960 Thomas Hull, Project Origami: Activities for Exploring Mathematics, A K Peters/CRC Press, 2006.
%H A304960 Franck Ramaharo, <a href="https://ramaharo.wordpress.com/2014/03/02/level-two-mosely-snowflake-sponge/">Level Two Mosely Snowflake Sponge</a>
%H A304960 Origami Resource Center, <a href="https://www.origami-resource-center.com/business-card-origami.html">Business Card Origami</a>
%H A304960 Origami Resource Center, <a href="https://www.origami-resource-center.com/mosely-snowflake-sponge-fractal-level-3.html">Mosely Snowflake Sponge Fractal (Level 3)</a>
%H A304960 The Institute For Figuring, <a href="http://www.theiff.org/exhibits/sponge.html">The Mosely Snowflake Sponge at the USC Libraries</a>
%H A304960 The Institute For Figuring, <a href="http://www.theiff.org/exhibits/USC%20Sponge%20Guide.pdf">USC Sponge Guide</a>
%H A304960 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mosely_snowflake">Mosely snowflake</a>
%H A304960 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (23,-90)
%F A304960 a(n) = (108*18^n + 48*5^n)/13.
%F A304960 a(n) = 18*a(n-1) - 48*5^(n - 1);
%F A304960 a(n) = 23*a(n-1) - 90*a(n-2), with a(0) = 12 and a(1) = 168.
%F A304960 G.f.: - 12*(9*x - 1)/((5*x - 1)*(18*x - 1)).
%F A304960 E.g.f.: (108*exp(18*x) + 48*exp(5*x))/13.
%e A304960 a(1) = 168 because 108 business cards are needed for the squeleton and 60 more for the panels (see guide in links).
%p A304960 seq((108*18^n + 48*5^n)/13, n = 0 .. 50);
%t A304960 LinearRecurrence[{23, -90}, {12, 168}, 50]
%o A304960 (Maxima) makelist((108*18^n + 48*5^n)/13, n, 0, 50);
%Y A304960 Cf. A212596 (Origami Menger sponge).
%K A304960 nonn,easy
%O A304960 0,1
%A A304960 _Franck Maminirina Ramaharo_, May 22 2018