A332189 a(n) = 8*(10^(2n+1)-1)/9 + 10^n.

9, 898, 88988, 8889888, 888898888, 88888988888, 8888889888888, 888888898888888, 88888888988888888, 8888888889888888888, 888888888898888888888, 88888888888988888888888, 8888888888889888888888888, 888888888888898888888888888, 88888888888888988888888888888, 8888888888888889888888888888888

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), A002282 (8*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332119 .. A332189 (variants with different "wing" digit 1, ..., 8).

Cf. A332180 .. A332187 (variants with different middle digit 0, ..., 7).

Programs

Maple

A332189 := n -> 8*(10^(2*n+1)-1)/9+10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]

PARI

apply( {A332189(n)=10^(n*2+1)\9*8+10^n}, [0..15])

Python

def A332189(n): return 10**(n*2+1)//9*8+10**n

Formula

a(n) = 8*A138148(n) + 9*10^n = A002282(2n+1) + 10^n.

G.f.: (9 - 101*x - 700*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.