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

1,1

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).

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

Mathematica

LinearRecurrence[{7, -14, 8}, {4, 8, 20}, 30] (* Harvey P. Dale, Sep 01 2023 *)

Prog

(PARI) a(n) = { (2^n + 2)*(2^n + 4)/6 } \\ Harry J. Smith, Jul 14 2009

Crossrefs

Cf. A007581, A002450, A028400.

Sequence in context: A357287 A371596 A115099 * A009333 A187010 A240149

Adjacent sequences: A060916 A060917 A060918 * A060920 A060921 A060922

Keyword

nonn,easy,changed

Author

Henry Bottomley, Apr 10 2001

Status

approved