A260846 a(n) = (-3 - 28*3^n + 73*15^n)/21.

2, 48, 770, 11696, 175874, 2639408, 39595010, 593936816, 8909087234, 133636413488, 2004546517250, 30068198703536, 451022983387394, 6765344759313968, 101480171415218690, 1522202571304807856, 22833038569801700354, 342495578547714252848, 5137433678217780035330

Offset

0,1

Comments

a(n) is the total number of holes at n iterations of a fractal starting with a pattern of 15 boxes and 2 nonsquare holes (see illustration in Links field).

Links

Colin Barker, Table of n, a(n) for n = 0..849

Kival Ngaokrajang, Illustration of initial terms

Index entries for linear recurrences with constant coefficients, signature (19, -63, 45).

Formula

a(0) = 2, a(n) = 15*a(n-1) + 2 + 16*3^(n-1) for n > 0.

a(n) = 2*15^n + 2*Sum_{i=0..n-1} 15^i*(1 + 8*3^(n-1-i)).

G.f.: 2*(8*x^2-5*x-1) / ((x-1)*(3*x-1)*(15*x-1)). - Colin Barker, Aug 01 2015

a(n) = 19*a(n-1) - 63*a(n-2) + 45*a(n-3) for n>2. - Colin Barker, Aug 20 2015

Mathematica

Table[(- 3 - 28 3^n + 73 15^n)/21, {n, 0, 20}] (* Vincenzo Librandi, Aug 22 2015 *)
LinearRecurrence[{19, -63, 45}, {2, 48, 770}, 20] (* Harvey P. Dale, Apr 18 2020 *)

Prog

(PARI) {for (n=0, 100, s=0; for (i=0, n-1, s=s+2*15^i*(1+8*3^(n-1-i))); a=s+2*15^n; print1(a, ", "))}
(PARI) Vec(2*(8*x^2-5*x-1)/((x-1)*(3*x-1)*(15*x-1)) + O(x^20)) \\ Colin Barker, Aug 01 2015
(Magma) [(-3-28*3^n+73*15^n)/21: n in [0..25]]; // Vincenzo Librandi, Aug 22 2015

Crossrefs

Sequence in context: A157057 A290690 A013523 * A009670 A024236 A119703

Adjacent sequences: A260843 A260844 A260845 * A260847 A260848 A260849

Keyword

nonn,easy

Author

Kival Ngaokrajang, Aug 01 2015

Extensions

Condensed title by Colin Barker, Aug 01 2015

Status

approved