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A002282
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a(n) = 8*(10^n - 1)/9.
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40
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0, 8, 88, 888, 8888, 88888, 888888, 8888888, 88888888, 888888888, 8888888888, 88888888888, 888888888888, 8888888888888, 88888888888888, 888888888888888, 8888888888888888, 88888888888888888, 888888888888888888, 8888888888888888888
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listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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If the initial term is omitted, might be called eightful (or hateful) numbers!
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LINKS
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FORMULA
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a(n) = 11a(n-1) - 10a(n-2), with a(0)=0, a(1)=8.
G.f.: 8x/((1-x)(1-10x)). (End)
E.g.f.: 8*(exp(9*x) - 1)*exp(x)/9.
a(n) = floor(8*10^n/9). (End)
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EXAMPLE
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Curious multiplications:
9*9 + 7 = 88;
98*9 + 6 = 888;
987*9 + 5 = 8888;
9876*9 + 4 = 88888;
98765*9 + 3 = 888888;
987654*9 + 2 = 8888888;
9876543*9 + 1 = 88888888;
98765432*9 + 0 = 888888888;
987654321*9 - 1 = 8888888888;
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MAPLE
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MATHEMATICA
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LinearRecurrence[{11, -10}, {0, 8}, 20] (* Harvey P. Dale, May 30 2013 *)
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PROG
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(PARI) { a=-4/5; for (n = 0, 200, a+=8*10^(n - 1); write("b002282.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 27 2009
(Python) def a(n): return int(8*(10**n - 1)/9) # Martin Gergov, Oct 19 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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