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Search: id:A055246
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| A055246 |
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Related to A005836. Used for boundaries of open intervals which have to be erased in the Cantor middle third set construction. |
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+0
5
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| 1, 7, 19, 25, 55, 61, 73, 79, 163, 169, 181, 187, 217, 223, 235, 241, 487, 493, 505, 511, 541, 547, 559, 565, 649, 655, 667, 673, 703, 709, 721, 727, 1459, 1465, 1477, 1483, 1513, 1519, 1531, 1537, 1621, 1627, 1639, 1645, 1675, 1681, 1693, 1699
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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At step number k >= 1 the 2^(k-1) open intervals which are erased from [0,1] in the Cantor middle third set construction are: I(k,n)=(a(n)/3^k,(1+a(n))/3^k), n=1,.,2^(k-1).
If g(n)=sum(i=0,n,i*binomial(n+i,i)^3*binomial(n,i)^2); m such that Mod(g(m),3)<>0 is same as a(n) www-ifm.math.uni-hannover.de/preprints/pr290.ps - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 08 2004
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LINKS
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R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(n)= 1+6*A005836(n-1), n >= 1.
a(n+1) = A074938(n) + A074939(n); A074938 : odd numbers in A005836, A074939 : even numbers in A005836 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005
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EXAMPLE
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k=1: (1/3, 2/3); k=2: (1/9, 2/9), (7/9, 8/9); k=3: (1/27, 2/27), (7/27, 8/27), (19/27, 20/27), (25/27, 26/27); ...
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PROGRAM
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(PARI) g(n)=sum(i=0, n, i*binomial(n+i, i)^3*binomial(n, i)^2); for (i=1, 2000, if(Mod(g(i), 3)<>0, print1(i, ", ")))
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CROSSREFS
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A005836, A055247.
a(n)=1+3*A005823(n-1), n>=1.
Adjacent sequences: A055243 A055244 A055245 this_sequence A055247 A055248 A055249
Sequence in context: A065749 A032642 A127633 this_sequence A003282 A006063 A038593
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 23 2000
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