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A332142
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a(n) = 4*(10^(2*n+1)-1)/9 - 2*10^n.
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1
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2, 424, 44244, 4442444, 444424444, 44444244444, 4444442444444, 444444424444444, 44444444244444444, 4444444442444444444, 444444444424444444444, 44444444444244444444444, 4444444444442444444444444, 444444444444424444444444444, 44444444444444244444444444444, 4444444444444442444444444444444
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listen;
history;
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..15.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
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FORMULA
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a(n) = 4*A138148(n) + 2*10^n = A002278(2n+1) - 2*10^n = 2*A332121(n).
G.f.: (2 + 202*x - 600*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
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MAPLE
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A332142 := n -> 4*(10^(2*n+1)-1)/9-2*10^n;
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MATHEMATICA
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Array[4 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
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PROG
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(PARI) apply( {A332142(n)=10^(n*2+1)\9*4-2*10^n}, [0..15])
(Python) def A332142(n): return 10**(n*2+1)//9*4-2*10**n
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CROSSREFS
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Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332112 .. A332192 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).
Sequence in context: A080392 A154541 A119120 * A109931 A352498 A326364
Adjacent sequences: A332139 A332140 A332141 * A332143 A332144 A332145
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KEYWORD
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nonn,base,easy
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AUTHOR
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M. F. Hasler, Feb 09 2020
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STATUS
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approved
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