A332184 a(n) = 8*(10^(2n+1)-1)/9 - 4*10^n.

4, 848, 88488, 8884888, 888848888, 88888488888, 8888884888888, 888888848888888, 88888888488888888, 8888888884888888888, 888888888848888888888, 88888888888488888888888, 8888888888884888888888888, 888888888888848888888888888, 88888888888888488888888888888, 8888888888888884888888888888888

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

Programs

Maple

A332184 := n -> 8*(10^(2*n+1)-1)/9-4*10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9- 4*10^# &, 15, 0]

PARI

apply( {A332184(n)=10^(n*2+1)\9*8-4*10^n}, [0..15])

Python

def A332184(n): return 10**(n*2+1)//9*8-4*10**n

Formula

a(n) = 8*A138148(n) + 4*10^n = A002282(2n+1)- 4*10^n = 4*A332121(n).

G.f.: (4 + 404*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.