

A260846


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


1



2, 48, 770, 11696, 175874, 2639408, 39595010, 593936816, 8909087234, 133636413488, 2004546517250, 30068198703536, 451022983387394, 6765344759313968, 101480171415218690, 1522202571304807856, 22833038569801700354, 342495578547714252848, 5137433678217780035330
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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(n1) + 2 + 16*3^(n1) for n > 0.
a(n) = 2*15^n + 2*Sum_{i=0..n1} 15^i*(1 + 8*3^(n1i)).
G.f.: 2*(8*x^25*x1) / ((x1)*(3*x1)*(15*x1)).  Colin Barker, Aug 01 2015
a(n) = 19*a(n1)  63*a(n2) + 45*a(n3) 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 *)


PROG

(PARI) {for (n=0, 100, s=0; for (i=0, n1, s=s+2*15^i*(1+8*3^(n1i))); a=s+2*15^n; print1(a, ", "))}
(PARI) Vec(2*(8*x^25*x1)/((x1)*(3*x1)*(15*x1)) + O(x^20)) \\ Colin Barker, Aug 01 2015
(MAGMA) [(328*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



