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A328916
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Number of n-digit decimal numbers containing 123 as a substring.
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1
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0, 0, 0, 1, 19, 280, 3699, 45971, 549430, 6390601, 72860039, 818050960, 9074118999, 99668329951, 1085865248550, 11749578366501, 126396115335059, 1352875288102040, 14417003302653899, 153043636911203931, 1619083493823937270, 17076417934936718801
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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See A322628 for the number of n-digit decimal numbers containing 12 as a substring.
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LINKS
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Michael Gutierrez, Table of n, a(n) for n = 0..997
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FORMULA
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a(n) = 10*a(n-1) + 9*10^(n-4) - a(n-3).
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EXAMPLE
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For n=6, there are a(6)=3699 six-digit numbers that contain 123 as a substring.
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PROG
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(Python)
a = [0, 0, 0, 1]
for i in range(0, 18):
a.append(10 * a[len(a) - 1] + 9 * 10 ** (len(a) - 4) - a[len(a) - 3])
print(a)
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CROSSREFS
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Cf. A322628.
Sequence in context: A197742 A322628 A322053 * A081045 A155017 A199245
Adjacent sequences: A328913 A328914 A328915 * A328917 A328918 A328919
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KEYWORD
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nonn,base,easy,changed
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AUTHOR
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Michael Gutierrez, Oct 30 2019
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STATUS
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approved
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