OFFSET
0,3
COMMENTS
Partial sums are in A014905. Also, the sequence is related to A014938 by A014938(n) = n*a(n) - Sum_{i=0..n-1} a(i) for n > 0. - Bruno Berselli, Nov 06 2012
For n >= 1, 4*a(n) is the total number of holes in a certain box fractal (start with 21 boxes, 4 holes) after n iterations. See illustration in links. - Kival Ngaokrajang, Jan 27 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..700
Kival Ngaokrajang, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (22,-21).
FORMULA
a(n) = floor(21^n/20).
G.f.: x/((1-x)*(1-21*x)). - Bruno Berselli, Nov 06 2012
a(n) = 22*a(n-1) - 21*a(n-2). - Vincenzo Librandi, Nov 07 2012
a(n) = 21*a(n-1) + 1. - Kival Ngaokrajang, Jan 27 2015
a(n) = a(n-1) + 21^(n-1), n >= 1, a(0) = 0. - Wolfdieter Lang, Feb 02 2015
E.g.f.: exp(11*x)*sinh(10*x)/10. - Elmo R. Oliveira, Aug 29 2024
MATHEMATICA
LinearRecurrence[{22, -21}, {0, 1}, 40] (* Vincenzo Librandi, Nov 07 2012 *)
PROG
(PARI) A218724(n)=21^n\20
(Magma) [n le 2 select n-1 else 22*Self(n-1) - 21*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved