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A332151 a(n) = 5*(10^(2*n+1)-1)/9 - 4*10^n.

%I A332151 #9 Mar 16 2021 13:58:45
%S A332151 1,515,55155,5551555,555515555,55555155555,5555551555555,
%T A332151 555555515555555,55555555155555555,5555555551555555555,
%U A332151 555555555515555555555,55555555555155555555555,5555555555551555555555555,555555555555515555555555555,55555555555555155555555555555,5555555555555551555555555555555
%N A332151 a(n) = 5*(10^(2*n+1)-1)/9 - 4*10^n.
%H A332151 Harvey P. Dale, <a href="/A332151/b332151.txt">Table of n, a(n) for n = 0..499</a>
%H A332151 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332151 a(n) = 5*A138148(n) + 10^n = A002279(2n+1) - 4*10^n.
%F A332151 G.f.: (1 + 404*x - 900*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332151 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332151 A332151 := n -> 5*(10^(2*n+1)-1)/9-4*10^n;
%t A332151 Array[5 (10^(2 # + 1)-1)/9 - 4*10^# &, 15, 0]
%t A332151 Table[With[{c=PadRight[{},n,5]},FromDigits[Join[c,{1},c]]],{n,0,20}] (* _Harvey P. Dale_, Mar 16 2021 *)
%o A332151 (PARI) apply( {A332151(n)=10^(n*2+1)\9*5-4*10^n}, [0..15])
%o A332151 (Python) def A332151(n): return 10**(n*2+1)//9*5-4*10**n
%Y A332151 Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
%Y A332151 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332151 Cf. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).
%Y A332151 Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).
%K A332151 nonn,base,easy
%O A332151 0,2
%A A332151 _M. F. Hasler_, Feb 09 2020