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A274755
Repunits with even indices multiplied by 99, i.e., 99*(11, 1111, 111111, 11111111, ...).
3
1089, 109989, 10999989, 1099999989, 109999999989, 10999999999989, 1099999999999989, 109999999999999989, 10999999999999999989, 1099999999999999999989, 109999999999999999999989, 10999999999999999999999989, 1099999999999999999999999989
OFFSET
1,1
COMMENTS
The reciprocals of the terms give a sequence of even growing periods, starting from 22, with delta = 22 (i.e., 22,44,66,88,110,132,...).
FORMULA
a(n) = 101*a(n-1) - 100*a(n-2), with a(0)= 1089 and a(1)= 109989.
G.f.: 1089*x/((1 - x)*(1 - 100*x)). - Ilya Gutkovskiy, Jul 04 2016
a(n) = 99*A099814(n). - Michel Marcus, Jul 04 2016
a(n) = 11*(10^(2*n)-1). - Robert Israel, Jul 06 2016
EXAMPLE
a(2) = 101*109989 - 100*1089 = 10999989.
MAPLE
A274755:= n-> 11*(10^(2*n) - 1) : seq(A274755(n), n=1..20);
MATHEMATICA
Array[99(10^(2 #)- 1)/9&, 15]
LinearRecurrence[{101, -100}, {1089, 109989}, 20] (* Vincenzo Librandi, Jul 07 2016 *)
PROG
(Magma) [11*(10^(2*n) - 1): n in [1..20]]:
(PARI) Vec(1089*x/((1-x)*(1-100*x)) + O(x^99)) \\ Altug Alkan, Jul 06 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rodolfo A. Fiorini, Jul 04 2016
STATUS
approved