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A137824
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Index at which A137823(n) occurs first in A137822 (gaps in numbers m such that 3 | sum( Catalan(k), k=1..2m)).
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7
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1, 3, 2, 4, 12, 8, 16, 48, 32, 64, 192, 128, 256, 768, 512, 1024, 3072, 2048, 4096, 12288, 8192, 16384, 49152, 32768, 65536, 196608, 131072, 262144, 786432, 524288, 1048576, 3145728, 2097152, 4194304, 12582912, 8388608, 16777216, 50331648
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OFFSET
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1,2
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COMMENTS
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Other characterization of the sequence: concatenate pattern (1,3,2) multiplying it by 4 after each concatenation step. Or: Start with 1,3,2, then iteratively append the whole sequence obtained so far multiplied by 4^(length of the sequence divided by 3)
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LINKS
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FORMULA
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If n=2 (mod 3) then a(n) = 3*2^[2(n-1)/3]; else a(n) = 2^[(2(n-1)/3].
a(n) = 4*a(n-3) for n>3. G.f.: x*(1+x)*(1+2*x)/(1-4*x^3). [Colin Barker, Aug 19 2012]
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PROG
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(PARI) A137824(n) = if( n%3==2, 3, 1)<<(2*(n-1)\3)
(PARI) a=[1, 3, 2]; for( i=1, 5, a=concat( a, 4^(#a/3)*a )); a
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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