A332148 - OEIS

%I #8 Feb 11 2020 08:13:01

%S 8,484,44844,4448444,444484444,44444844444,4444448444444,

%T 444444484444444,44444444844444444,4444444448444444444,

%U 444444444484444444444,44444444444844444444444,4444444444448444444444444,444444444444484444444444444,44444444444444844444444444444,4444444444444448444444444444444

%N a(n) = 4*(10^(2*n+1)-1)/9 + 4*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) = 4*A138148(n) + 8*10^n = A002278(2n+1) + 4*10^n = 4*A332112(n).

%F G.f.: (8 - 404*x)/((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 A332148 := n -> 4*((10^(2*n+1)-1)/9+10^n);

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

%o (PARI) apply( {A332148(n)=(10^(n*2+1)\9+10^n)*4}, [0..15])

%o (Python) def A332148(n): return (10**(n*2+1)//9+10**n)*4

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).

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

%Y Cf. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).

%Y Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

%K nonn,base,easy

%O 0,1

%A _M. F. Hasler_, Feb 09 2020