A332183 -id:A332183 - cp's OEIS frontend

A332193 a(n) = 10^(2n+1) - 1 - 6*10^n.

3, 939, 99399, 9993999, 999939999, 99999399999, 9999993999999, 999999939999999, 99999999399999999, 9999999993999999999, 999999999939999999999, 99999999999399999999999, 9999999999993999999999999, 999999999999939999999999999, 99999999999999399999999999999, 9999999999999993999999999999999

Offset: 0

M. F. Hasler, Feb 08 2020

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

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).

Maple
```
A332193 := n -> 10^(n*2+1)-1-6*10^n;
```

Array[ 10^(2 # + 1) - 1 - 6*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{3,939,99399},20] (* Harvey P. Dale, Jan 19 2024 *)

apply( {A332193(n)=10^(n*2+1)-1-6*10^n}, [0..15])

def A332193(n): return 10**(n*2+1)-1-6*10^n

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.

cp's OEIS Frontend

A332193 a(n) = 10^(2n+1) - 1 - 6*10^n.

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