A240846 a(0)=0, a(1)=1, a(n) = a(n-1)*12 + 13.

0, 1, 25, 313, 3769, 45241, 542905, 6514873, 78178489, 938141881, 11257702585, 135092431033, 1621109172409, 19453310068921, 233439720827065, 2801276649924793, 33615319799097529, 403383837589170361, 4840606051070044345, 58087272612840532153

Offset

0,3

Comments

a(n) is the total number of holes in a dodecaflake after n iterations.

Links

G. C. Greubel, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (13,-12).

Formula

From Colin Barker, Apr 13 2014: (Start)

a(n) = (2^(2*n+1)*3^n - 13)/11 for n>0.

a(n) = 13*a(n-1) - 12*a(n-2) for n>2.

G.f.: x*(1+12*x) /((1-x)*(1-12*x)). (End).

E.g.f.: (11 - 13*exp(x) + 2*exp(12*x))/11. - G. C. Greubel, Feb 06 2020

Maple

A240846:=n->`if`(n=0, 0, (2^(1+2*n)*3^n-13)/11); seq(A240846(n), n=0..20); # Wesley Ivan Hurt, Apr 13 2014

Mathematica

Join[{0}, NestList[12#+13&, 1, 20]] (* or *) LinearRecurrence[{13, -12}, {0, 1, 25}, 30] (* Harvey P. Dale, Sep 08 2017 *)

Prog

(PARI) {a(n)=if(n<=0, 0, if(n<2, 1, a(n-1)*12+13))}
for(n=0, 20, print1(a(n), ", "))
(Magma) [0] cat [(2^(2*n+1)*3^n - 13)/11: n in [1..20]]; // G. C. Greubel, Feb 06 2020
(Sage) [0]+[(2^(2*n+1)*3^n - 13)/11 for n in (1..20)] # G. C. Greubel, Feb 06 2020
(GAP) Concatenation([0], List([1..20], n-> (2^(2*n+1)*3^n - 13)/11 )); # G. C. Greubel, Feb 06 2020

Crossrefs

Cf. A240735.

Sequence in context: A264274 A278876 A053805 * A228255 A125437 A250318

Adjacent sequences: A240843 A240844 A240845 * A240847 A240848 A240849

Keyword

nonn,easy

Author

Kival Ngaokrajang, Apr 13 2014

Extensions

Name changed by Colin Barker, Apr 13 2014

Status

approved