A332182 a(n) = 8*(10^(2n+1)-1)/9 - 6*10^n.

2, 828, 88288, 8882888, 888828888, 88888288888, 8888882888888, 888888828888888, 88888888288888888, 8888888882888888888, 888888888828888888888, 88888888888288888888888, 8888888888882888888888888, 888888888888828888888888888, 88888888888888288888888888888, 8888888888888882888888888888888

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 only).

Cf. A332112 .. A332192 (variants with different repeated digit 1, ..., 9).

Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

Programs

Maple

A332182 := n -> 8*(10^(2*n+1)-1)/9-6*10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9 - 6*10^# &, 15, 0]

PARI

apply( {A332182(n)=10^(n*2+1)\9*8-6*10^n}, [0..15])

Python

def A332182(n): return 10**(n*2+1)//9*8-6*10**n

Formula

a(n) = 8*A138148(n) + 2*10^n = A002282(2n+1)- 6*10^n.

G.f.: (2 + 606*x - 1400*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.