A332180 a(n) = 8*(10^(2n+1)-1)/9 - 8*10^n.

0, 808, 88088, 8880888, 888808888, 88888088888, 8888880888888, 888888808888888, 88888888088888888, 8888888880888888888, 888888888808888888888, 88888888888088888888888, 8888888888880888888888888, 888888888888808888888888888, 88888888888888088888888888888, 8888888888888880888888888888888

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), A002113 (palindromes).

Cf. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).

Cf. A332181 .. A332189 (variants with different middle digit 1, ..., 9).

Subsequence of A006072 (numbers with mirror symmetry about middle), A153806 (strobogrammatic cyclops numbers), and A204095 (numbers whose decimal digits are in {0,8}).

Programs

Maple

A332180 := n -> 8*((10^(2*n+1)-1)/9-10^n);

Mathematica

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

PARI

apply( {A332180(n)=(10^(n*2+1)\9-10^n)*8}, [0..15])

Python

def A332180(n): return (10**(n*2+1)//9-10**n)*8

Formula

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

G.f.: 8*x*(101 - 200*x)/((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.: 8*exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024