%I #10 Jul 13 2024 21:13:37

%S 6,565,55655,5556555,555565555,55555655555,5555556555555,

%T 555555565555555,55555555655555555,5555555556555555555,

%U 555555555565555555555,55555555555655555555555,5555555555556555555555555,555555555555565555555555555,55555555555555655555555555555,5555555555555556555555555555555

%N a(n) = 5*(10^(2*n+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) = 5*A138148(n) + 6*10^n = A002279(2n+1) + 10^n.

%F G.f.: (6 - 101*x - 400*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.

%F E.g.f.: exp(x)*(50*exp(99*x) + 9*exp(9*x) - 5)/9. - _Stefano Spezia_, Jul 13 2024

%p A332156 := n -> 5*(10^(2*n+1)-1)/9+10^n;

%t Array[5 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]

%o (PARI) apply( {A332156(n)=10^(n*2+1)\9*5+10^n}, [0..15])

%o (Python) def A332156(n): return 10**(n*2+1)//9*5+10**n

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).

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

%Y Cf. A332116 .. A332196 (variants with different repeated digit 1, ..., 9).

%Y Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

%K nonn,base,easy

%O 0,1

%A _M. F. Hasler_, Feb 09 2020