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Search: id:A033146
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| A033146 |
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Base 10 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0. |
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+0
1
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| 1, 10, 100, 1001, 10010, 100100, 1001001, 10010010, 100100100, 1001001001, 10010010010, 100100100100, 1001001001001, 10010010010010, 100100100100100
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.: 1/((1-x^3)(1-10x)); a(n)=10a(n-1)+a(n-3)-10a(n-4); a(n)=sum{k=0..floor(n/3), 10^(n-3k)} [offset 0]; a(n)=sum{k=0..n, 10^k*(cos(2*pi*(n-k)/3+pi/3)/3+sqrt(3)sin(2*pi*(n-k)/3+pi/3)/3+1/3)} [offset 0]. - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
a(n)=10*a(n-1)+(1/9)*{(n mod 3)+4*[(n+1) mod 3]-2*[(n+2) mod 3]}, with a(0)=0. Closed form: a(n)=-(1/27)+(1000/999)*10^n+(5/333)*I*sqrt(3)*{[ -(1/2)-(1/2)*I*sqrt(3)]^n-[ -(1/2)+(1/2)*I*sqrt(3)]^n}+(2/111)*{[ -(1/2)-(1/2)*I*sqrt(3)]^n+[ -(1/2)+(1/2)*I*sqrt(3)]^n}, with n>=1 [From Paolo P. Lava (ppl(AT)spl.at), Jul 30 2009]
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CROSSREFS
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Sequence in context: A138824 A138823 A145442 this_sequence A118256 A102397 A132347
Adjacent sequences: A033143 A033144 A033145 this_sequence A033147 A033148 A033149
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KEYWORD
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nonn,base
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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