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Search: id:A106191
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| A106191 |
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Expansion of sqrt(1-4x)/(1-x). |
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+0
10
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| 1, -1, -3, -7, -17, -45, -129, -393, -1251, -4111, -13835, -47427, -164999, -581023, -2066823, -7415703, -26805393, -97520733, -356810313, -1312087713, -4846614093, -17974854933, -66907388973, -249872516253, -935991743553, -3515800038201, -13239692841105
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums of number triangle A106190. Partial sums of A002420.
For n>=1 onward, the absolute values give also the iterates of A122237, starting from 0. (A122237(0), A122237(A122237(0)), A122237(A122237(A122237(0))), ...), this stems from the fact that the sequence gives the positions of terms with binary expansion 1(10){n-1}0 in A014486 (see A080675).
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FORMULA
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a(n)=sum{k=0..n, binomial(2k, k)/(1-2k)}
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CROSSREFS
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|a(n)| = A080300(A080675(n)) = A075161(A001348(n)) (for n>=1) = A075163(A000244(A008578(n-2))) = A014137(n-1)+A014138(n-2) = 2*A014137(n-1)-1, for n>=2. (Because binomial(2n+2, n+1)/(2n+1) = 2*A000108(n))
Sequence in context: A018025 A018026 A087953 this_sequence A062810 A113985 A151265
Adjacent sequences: A106188 A106189 A106190 this_sequence A106192 A106193 A106194
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 24 2005
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EXTENSIONS
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Barry's formula made more succinct, as well as comments regarding interpretation as absolute values added by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Sep 14 2006.
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