OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..450
Wikipedia, Kynea number
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
FORMULA
a(n) = -1/9+10^(1+n)/9+100^n.
a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3).
G.f.: -x*(2000*x^2-2210*x+111) / ((x-1)*(10*x-1)*(100*x-1)).
EXAMPLE
a(3) is 1001111 because A093069(3) = 79 which is 1001111 in base 2.
MAPLE
MATHEMATICA
Table[-1/9 + 10^(1 + n)/9 + 100^n, {n, 15}] (* Wesley Ivan Hurt, Jul 09 2014 *)
LinearRecurrence[{111, -1110, 1000}, {111, 10111, 1001111}, 20] (* Harvey P. Dale, Dec 11 2014 *)
PROG
(PARI) vector(100, n, -1/9+10^(1+n)/9+100^n)
(PARI) Vec(-x*(2000*x^2-2210*x+111)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100))
(Magma) [-1/9 + 10^(1 + n)/9 + 100^n : n in [1..15]]; // Wesley Ivan Hurt, Jul 09 2014
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Colin Barker, Jul 08 2014
STATUS
approved