A332196 a(n) = 10^(2n+1) - 1 - 3*10^n.

6, 969, 99699, 9996999, 999969999, 99999699999, 9999996999999, 999999969999999, 99999999699999999, 9999999996999999999, 999999999969999999999, 99999999999699999999999, 9999999999996999999999999, 999999999999969999999999999, 99999999999999699999999999999

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. A332116 .. A332186 (variants with different repeated digit 1, ..., 8).

Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).

Programs

Maple

A332196 := n -> 10^(n*2+1)-1-3*10^n;

Mathematica

Array[ 10^(2 # + 1) - 1 - 3*10^# &, 15, 0]
FromDigits/@Table[Join[PadLeft[{6},n,9],PadRight[{},n-1,9]],{n,30}] (* or *) LinearRecurrence[{111,-1110,1000},{6,969,99699},30] (* Harvey P. Dale, May 03 2021 *)

PARI

apply( {A332196(n)=10^(n*2+1)-1-3*10^n}, [0..15])

Python

def A332196(n): return 10**(n*2+1)-1-3*10^n

Formula

a(n) = 9*A138148(n) + 6*10^n.

G.f.: (6 + 303*x - 1200*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.

E.g.f.: exp(x)*(10*exp(99*x) - 3*exp(9*x) - 1). - Stefano Spezia, Jul 13 2024