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A109344
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a(n) consists of n 4's, n-1 8's and a single 9.
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2
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49, 4489, 444889, 44448889, 4444488889, 444444888889, 44444448888889, 4444444488888889, 444444444888888889, 44444444448888888889, 4444444444488888888889, 444444444444888888888889
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence consists of perfect squares. The square roots are in A073552.
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REFERENCES
| Italo Ghersi, Matematica dilettevole e curiosa, pag.112, Hoepli, Milano, 1967 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 31 2008]
Paul Zeitz, The Art and Craft of Problem Solving, John Wiley and Sons, Inc., New York, 1999.
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LINKS
| StackExchange, History of 'Show that 44...88...9 is a perfect square'.
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FORMULA
| a(1)=49; a(n) = 4*(sum(i=n...2n-1)10^i)+8*sum(i=1...n-1)10^i)+9, n>=2
a(n)=111*a(n-1)-1110*a(n-2)+1000*a(n-3) = (4*100^n+4*10^n+1)/9. G.f.: x*(49-950*x+1000*x^2)/((1-x)*(100*x-1)*(10*x-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 06 2009]
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EXAMPLE
| a(5)=4444488889 because the first 5 terms are 4's, the next 5-1=4 terms are 8's and the last digit is 9.
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MAPLE
| a:=n->4*sum('10^i', 'i'=n..2*n-1)+8*sum('10^i', 'i'=1..n-1)+9;
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CROSSREFS
| Cf. A073552.
Sequence in context: A123841 A014773 A132539 * A129207 A053772 A075416
Adjacent sequences: A109341 A109342 A109343 * A109345 A109346 A109347
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KEYWORD
| nonn
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AUTHOR
| Nicholas Protonotarios (protost(AT)hotmail.com), Aug 21 2005
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