A060919 Number of corners in a 4-sided fractal.
4, 8, 20, 60, 204, 748, 2860, 11180, 44204, 175788, 701100, 2800300, 11193004, 44755628, 178989740, 715893420, 2863442604, 11453508268, 45813508780, 183252986540, 733009849004, 2932035201708, 11728132418220, 46912512895660, 187650018028204, 750600005003948, 3002399885798060
Offset: 1
Links
- Harry J. Smith, Table of n, a(n) for n=1,...,200
- Henry Bottomley, Illustration of initial terms
- Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
Programs
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Mathematica
LinearRecurrence[{7,-14,8},{4,8,20},30] (* Harvey P. Dale, Sep 01 2023 *) -
PARI
a(n) = { (2^n + 2)*(2^n + 4)/6 } \\ Harry J. Smith, Jul 14 2009
Formula
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).
From Colin Barker, Nov 28 2012: (Start)
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)). (End)
E.g.f.: (exp(4*x) + 6*exp(2*x) + 8*exp(x) - 15)/6. - Stefano Spezia, Dec 26 2024