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A332190
a(n) = 10^(2n+1) - 1 - 9*10^n.
16
0, 909, 99099, 9990999, 999909999, 99999099999, 9999990999999, 999999909999999, 99999999099999999, 9999999990999999999, 999999999909999999999, 99999999999099999999999, 9999999999990999999999999, 999999999999909999999999999, 99999999999999099999999999999, 9999999999999990999999999999999
OFFSET
0,2
FORMULA
a(n) = 9*A138148(n) = A002283(2n+1) - A011557(n).
G.f.: 9*x*(101 - 200*x)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
MAPLE
A332190 := n -> 10^(2*n+1)-1-9*10^n;
MATHEMATICA
Array[10^(2 # + 1)-1-9*10^# &, 15, 0]
LinearRecurrence[{111, -1110, 1000}, {0, 909, 99099}, 20] (* Harvey P. Dale, May 28 2021 *)
PROG
(PARI) apply( {A332190(n)=10^(n*2+1)-1-9*10^n}, [0..15])
(Python) def A332190(n): return 10**(n*2+1)-1-9*10^n
CROSSREFS
Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332120 .. A332180 (variants with different repeated digit 2, ..., 8).
Cf. A332191 .. A332197, A181965 (variants with different middle digit 1, ..., 8).
Sequence in context: A214001 A252136 A216930 * A015278 A352441 A210170
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 08 2020
STATUS
approved