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Search: id:A073711
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| A073711 |
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Sequence whose convolution produces all odd terms of itself, while the even terms are equal to the sequence. |
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2
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| 1, 1, 1, 2, 1, 3, 2, 6, 1, 7, 3, 12, 2, 16, 6, 26, 1, 31, 7, 42, 3, 59, 12, 72, 2, 104, 16, 116, 6, 184, 26, 186, 1, 303, 31, 282, 7, 497, 42, 406, 3, 783, 59, 612, 12, 1224, 72, 840, 2, 1856, 104, 1232, 16, 2784, 116, 1656, 6, 4136, 184, 2376, 26, 6008, 186, 3138, 1
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Let a(0)=1, then a(2^k)=1, a((2m+1)2^k)=a(2m+1) and a((2m)2^k)=a(m) where m>=0, k>=0. Let f(x) = sum_{n=0..inf} a(n) x^n, then f(x) = sum_{n=0..inf} a(2n) x^n, and f(x)^2 = sum_{n=0..inf} a(2n+1) x^n, and so f(x) satisfies the functional equation f(x) = f(x^2)*(1 + x*f(x^2)).
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EXAMPLE
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a(0)=1, a(2^k)=1, a(3*2^k)=2, a(5*2^k)=3, a(7*2^k)=6, a(9*2^k)=7, for k>=0. Convolution of {1,1,1,2,1,3,2,6,1,7,3,12,2,16,...} = {1,2,3,6,7,12,16,...}, which forms all the odd terms.
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CROSSREFS
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Sequence in context: A062951 A014000 A075257 this_sequence A071690 A114653 A069481
Adjacent sequences: A073708 A073709 A073710 this_sequence A073712 A073713 A073714
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 05 2002
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