A332147 - OEIS

%I #10 Mar 08 2022 15:04:00

%S 7,474,44744,4447444,444474444,44444744444,4444447444444,

%T 444444474444444,44444444744444444,4444444447444444444,

%U 444444444474444444444,44444444444744444444444,4444444444447444444444444,444444444444474444444444444,44444444444444744444444444444,4444444444444447444444444444444

%N a(n) = 4*(10^(2*n+1)-1)/9 + 3*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) + 7*10^n = A002278(2n+1) + 3*10^n.

%F G.f.: (7 - 303*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 A332147 := n -> 4*(10^(2*n+1)-1)/9+3*10^n;

%t Array[4 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]

%t LinearRecurrence[{111,-1110,1000},{7,474,44744},20] (* _Harvey P. Dale_, Mar 08 2022 *)

%o (PARI) apply( {A332147(n)=10^(n*2+1)\9*4+3*10^n}, [0..15])

%o (Python) def A332147(n): return 10**(n*2+1)//9*4+3*10**n

%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. A332117 .. A332197 (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