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Search: id:A047855
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| 1, 2, 12, 112, 1112, 11112, 111112, 1111112, 11111112, 111111112, 1111111112, 11111111112, 111111111112, 1111111111112, 11111111111112, 111111111111112, 1111111111111112
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Range of A164898, apart from first term. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 30 2009]
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FORMULA
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(10^n + 8)/9. - Ralf Stephan, Feb 14 2004
a(0)=1, a(1)=2, a(n)=11*a(n-1)-10*a(n-2) for n>1. - Lambert Klasen (lambert.klasen(AT)gmx.net), Jan 28 2005
G.f.: (1-9x)/(1-11x+10x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 05 2009]
a(n)=10*a(n-1)-8 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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EXAMPLE
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For n=2, a(2)=10*1-8=2; n=3, a(3)=10*2-8=12; n=4, a(4)=10*12-8=112 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=10*a[n-1]+1 od: seq(a[n]+1, n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
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PROGRAM
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(PARI) a(n)=if(n==0, 1, if(n==1, 2, 11*a(n-1)-10*a(n-2))) for(i=0, 10, print1(a(i), ", ")) (Klasen)
(Other) sage: [gaussian_binomial(n, 1, 10)+1 for n in xrange(0, 17)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
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CROSSREFS
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n-th difference of a(n), a(n-1), ..., a(0) is 9^(n-1) for n=1, 2, 3, ...
Sequence in context: A126778 A158832 A102659 this_sequence A009232 A124213 A143134
Adjacent sequences: A047852 A047853 A047854 this_sequence A047856 A047857 A047858
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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