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%I #6 Feb 11 2020 08:08:29
%S 2,424,44244,4442444,444424444,44444244444,4444442444444,
%T 444444424444444,44444444244444444,4444444442444444444,
%U 444444444424444444444,44444444444244444444444,4444444444442444444444444,444444444444424444444444444,44444444444444244444444444444,4444444444444442444444444444444
%N a(n) = 4*(10^(2*n+1)-1)/9 - 2*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) + 2*10^n = A002278(2n+1) - 2*10^n = 2*A332121(n).
%F G.f.: (2 + 202*x - 600*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 A332142 := n -> 4*(10^(2*n+1)-1)/9-2*10^n;
%t Array[4 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
%o (PARI) apply( {A332142(n)=10^(n*2+1)\9*4-2*10^n}, [0..15])
%o (Python) def A332142(n): return 10**(n*2+1)//9*4-2*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. A332112 .. A332192 (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
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