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A332154
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a(n) = 5*(10^(2*n+1)-1)/9 - 10^n.
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1
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4, 545, 55455, 5554555, 555545555, 55555455555, 5555554555555, 555555545555555, 55555555455555555, 5555555554555555555, 555555555545555555555, 55555555555455555555555, 5555555555554555555555555, 555555555555545555555555555, 55555555555555455555555555555, 5555555555555554555555555555555
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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) = 5*A138148(n) + 4*10^n = A002279(2n+1) - 10^n.
G.f.: (4 + 101*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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A332154 := n -> 5*(10^(2*n+1)-1)/9-10^n;
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MATHEMATICA
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Array[5 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
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PROG
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(PARI) apply( {A332154(n)=10^(n*2+1)\9*5-10^n}, [0..15])
(Python) def A332154(n): return 10**(n*2+1)//9*5-10**n
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CROSSREFS
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Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332114 .. A332194 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).
Sequence in context: A209608 A159367 A012770 * A202032 A267066 A159530
Adjacent sequences: A332151 A332152 A332153 * A332155 A332156 A332157
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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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