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A332193
a(n) = 10^(2n+1) - 1 - 6*10^n.
7
3, 939, 99399, 9993999, 999939999, 99999399999, 9999993999999, 999999939999999, 99999999399999999, 9999999993999999999, 999999999939999999999, 99999999999399999999999, 9999999999993999999999999, 999999999999939999999999999, 99999999999999399999999999999, 9999999999999993999999999999999
OFFSET
0,1
FORMULA
a(n) = 9*A138148(n) + 3*10^n = A002283(2n+1) - 6*10^n.
G.f.: (3 + 606*x - 1500*x^2)/((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
A332193 := n -> 10^(n*2+1)-1-6*10^n;
MATHEMATICA
Array[ 10^(2 # + 1) - 1 - 6*10^# &, 15, 0]
LinearRecurrence[{111, -1110, 1000}, {3, 939, 99399}, 20] (* Harvey P. Dale, Jan 19 2024 *)
PROG
(PARI) apply( {A332193(n)=10^(n*2+1)-1-6*10^n}, [0..15])
(Python) def A332193(n): return 10**(n*2+1)-1-6*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. A332113 .. A332183 (variants with different repeated digit 1, ..., 8).
Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
Sequence in context: A199040 A094592 A210768 * A167058 A167067 A324443
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 08 2020
STATUS
approved