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A060919 Number of corners in a 4-sided fractal. 6


%S 4,8,20,60,204,748,2860,11180,44204,175788,701100,2800300,11193004,

%T 44755628,178989740,715893420,2863442604,11453508268,45813508780,

%U 183252986540,733009849004,2932035201708,11728132418220,46912512895660

%N Number of corners in a 4-sided fractal.

%H Harry J. Smith, <a href="/A060919/b060919.txt">Table of n, a(n) for n=1,...,200</a>

%H H. Bottomley, <a href="/A060919/a060919.gif">Illustration of initial terms</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).

%F a(n) =4^n/6+2^n+4/3 =(2^n+2)*(2^n+4)/6 =4*A007581(n-1) =4(a(n-1)-1)-2^n =A028400(n-1)-A002450(n-1)

%F a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3). G.f.: -4*x*(5*x^2-5*x+1) / ((x-1)*(2*x-1)*(4*x-1)). [_Colin Barker_, Nov 28 2012]

%o (PARI) { for (n=1, 200, write("b060919.txt", n, " ", (2^n + 2)*(2^n + 4)/6); ) } \\ _Harry J. Smith_, Jul 14 2009

%K nonn,easy

%O 1,1

%A _Henry Bottomley_, Apr 10 2001

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Last modified November 23 16:18 EST 2020. Contains 338590 sequences. (Running on oeis4.)