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A332121
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a(n) = 2*(10^(2n+1)-1)/9 - 10^n.
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12
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1, 212, 22122, 2221222, 222212222, 22222122222, 2222221222222, 222222212222222, 22222222122222222, 2222222221222222222, 222222222212222222222, 22222222222122222222222, 2222222222221222222222222, 222222222222212222222222222, 22222222222222122222222222222, 2222222222222221222222222222222
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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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) = 2*A138148(n) + 1*10^n = A002276(2n+1) - 10^n.
G.f.: (1 + 101*x - 300*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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A332121 := n -> 2*(10^(2*n+1)-1)/9-10^n;
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MATHEMATICA
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Array[2 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
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PROG
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(PARI) apply( {A332121(n)=10^(n*2+1)\9*2-10^n}, [0..15])
(Python) def A332121(n): return 10**(n*2+1)//9*2-10**n
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CROSSREFS
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Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).
Cf. A332131 .. A332191 (variants with different repeated digit 3, ..., 9).
Sequence in context: A344423 A238023 A204299 * A083962 A007942 A210257
Adjacent sequences: A332118 A332119 A332120 * A332122 A332123 A332124
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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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