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

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Links

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

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).

Programs

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 *)

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

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.