A332123 - OEIS

%I #7 Feb 11 2020 08:00:31

%S 3,232,22322,2223222,222232222,22222322222,2222223222222,

%T 222222232222222,22222222322222222,2222222223222222222,

%U 222222222232222222222,22222222222322222222222,2222222222223222222222222,222222222222232222222222222,22222222222222322222222222222,2222222222222223222222222222222

%N a(n) = 2*(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) = 2*A138148(n) + 3*10^n = A002276(2n+1) + 10^n.

%F G.f.: (3 - 101*x - 100*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 A332123 := n -> 2*(10^(2*n+1)-1)/9+10^n;

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

%o (PARI) apply( {A332123(n)=10^(n*2+1)\9*2+10^n}, [0..15])

%o (Python) def A332123(n): return 10**(n*2+1)//9*2+10**n

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).

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

%Y Cf. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).

%Y Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

%K nonn,base,easy

%O 0,1

%A _M. F. Hasler_, Feb 09 2020