A241271 a(n) = 6*a(n-1) + 3*(2^(n-2)-1) for n > 2, a(0)=a(1)=a(2)=0.

0, 0, 0, 3, 27, 183, 1143, 6951, 41895, 251751, 1511271, 9069159, 54418023, 326514279, 1959097959, 11754612327, 70527723111, 423166436967, 2538998818407, 15233993303655, 91403960608359, 548423765223015, 3290542594483815, 19743255573194343, 118459533451748967

Offset: 0

Author

Kival Ngaokrajang, Apr 18 2014

Keywords

• nonn
• easy

Comments

a(n) is the total number of irregular polygon holes of a triflake-like fractal (A240916) after n iterations. A240916(n) - a(n) is the total number of rhombic holes.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Kival Ngaokrajang, Illustration of initial terms
• Kival Ngaokrajang, Illustration for n = 5
• Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

Crossrefs

Cf. A240916.

Programs

Maple

A241271:=n->`if`(n=0, 0, (24-15*2^n+6^n)/40); seq(A241271(n), n=0..40); # Wesley Ivan Hurt, Apr 19 2014

Mathematica

CoefficientList[Series[-3 x^3/((x - 1) (2 x - 1) (6 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 19 2014 *)
LinearRecurrence[{9,-20,12},{0,0,0,3},30] (* Harvey P. Dale, Dec 28 2021 *)

PARI

a(n) = if(n<=0,0,if(n<2,0,if(n<3,0,a(n-1)*6+3*(2^(n-2)-1))))
       for(n=0,100,print1(a(n),", "))

PARI

concat([0,0,0], Vec(-3*x^3/((x-1)*(2*x-1)*(6*x-1)) + O(x^100))) \\ Colin Barker, Apr 18 2014

Formula

a(n) = (24-15*2^n+6^n)/40 for n>0. G.f.: -3*x^3 / ((x-1)*(2*x-1)*(6*x-1)). - Colin Barker, Apr 18 2014