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Search: id:A053541
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| 1, 20, 300, 4000, 50000, 600000, 7000000, 80000000, 900000000, 10000000000, 110000000000, 1200000000000, 13000000000000, 140000000000000, 1500000000000000, 16000000000000000, 170000000000000000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This sequence gives the number of 1's (or any other digit) required to write all integers of n or fewer digits. It is thus A094798 for n=9, 99, 999, .... Another formula: a(n) = 10*a(n-1)+10(n-1) a(n) = Sum_{k=1...n} k*C(n,k)*9^(n-k) - Jason D. W. Taff (jtaff(AT)jburroughs.org), Dec 05 2004
With a different offset, number of n-permutations of 11 objects: p, q, r, s, t, u, v, w, z, x, y with repetition allowed, containing exactly one u. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 28 2007
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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F. Ellermann, Illustration of binomial transforms
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FORMULA
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a(n)=20a(n-1)-100a(n-2); a(0)=1; n>0.
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MAPLE
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seq(seq(binomial(i, j)*10^(i-1), j =i-1), i=1..17); # - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 28 2007
SAGE:[lucas_number2(n, 10, 0)*binomial(n, 1)/10for n in xrange(1, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
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CROSSREFS
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Cf. A001787, A053464 and A053469.
Cf. A094798.
Cf. A038303.
Sequence in context: A016255 A138794 A077758 this_sequence A004345 A001755 A016190
Adjacent sequences: A053538 A053539 A053540 this_sequence A053542 A053543 A053544
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Jan 15 2000
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001
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