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A332126
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a(n) = 2*(10^(2n+1)-1)/9 + 4*10^n.
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3
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6, 262, 22622, 2226222, 222262222, 22222622222, 2222226222222, 222222262222222, 22222222622222222, 2222222226222222222, 222222222262222222222, 22222222222622222222222, 2222222222226222222222222, 222222222222262222222222222, 22222222222222622222222222222, 2222222222222226222222222222222
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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) = 2*A138148(n) + 6*10^n = A002276(2n+1) + 4*10^n = 2*A332113(n).
G.f.: (6 - 404*x + 200*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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A332126 := n -> 2*(10^(2*n+1)-1)/9+4*10^n;
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MATHEMATICA
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Array[2 (10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]
Table[FromDigits[Join[PadRight[{}, n, 2], {6}, PadRight[{}, n, 2]]], {n, 0, 20}] (* or *) LinearRecurrence[{111, -1110, 1000}, {6, 262, 22622}, 20] (* Harvey P. Dale, Oct 17 2021 *)
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PROG
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(PARI) apply( {A332126(n)=10^(n*2+1)\9*2+4*10^n}, [0..15])
(Python) def A332126(n): return 10**(n*2+1)//9*2+4*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. A332116 .. A332196 (variants with different repeated digit 1, ..., 9).
Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).
Sequence in context: A225166 A003384 A316393 * A229579 A033289 A244493
Adjacent sequences: A332123 A332124 A332125 * A332127 A332128 A332129
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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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