A332189 - OEIS

%I #7 Feb 11 2020 08:30:44

%S 9,898,88988,8889888,888898888,88888988888,8888889888888,

%T 888888898888888,88888888988888888,8888888889888888888,

%U 888888888898888888888,88888888888988888888888,8888888888889888888888888,888888888888898888888888888,88888888888888988888888888888,8888888888888889888888888888888

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

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

%F G.f.: (9 - 101*x - 700*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).

%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

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

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

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

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

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).

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

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

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

%K nonn,base,easy

%O 0,1

%A _M. F. Hasler_, Feb 08 2020