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A332143
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a(n) = 4*(10^(2*n+1)-1)/9 - 10^n.
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2
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3, 434, 44344, 4443444, 444434444, 44444344444, 4444443444444, 444444434444444, 44444444344444444, 4444444443444444444, 444444444434444444444, 44444444444344444444444, 4444444444443444444444444, 444444444444434444444444444, 44444444444444344444444444444, 4444444444444443444444444444444
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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) + 3*10^n = A002278(2n+1) - 10^n.
G.f.: (3 + 101*x - 500*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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A332143 := n -> 4*(10^(2*n+1)-1)/9-10^n;
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MATHEMATICA
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Array[4 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
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PROG
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(PARI) apply( {A332143(n)=10^(n*2+1)\9*4-10^n}, [0..15])
(Python) def A332143(n): return 10**(n*2+1)//9*4-10**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. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).
Sequence in context: A229751 A172859 A087771 * A277234 A269553 A086207
Adjacent sequences: A332140 A332141 A332142 * A332144 A332145 A332146
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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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