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Search: id:A083318
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| A083318 |
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a(0) = 1; for n>0, a(n) = 2^n+1. |
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+0
7
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| 1, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Inverse binomial transform of A005056.
Also, A000533 interpreted as binary numbers, written in base 10. Numbers whose representation in base 2 is has n+1 digits and the digit "1" is the initial and final digit and if n>1 then the internal digits are "0" (See example). - Omar E. Pol (info(AT)polprimos.com), Feb 24 2008
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FORMULA
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a(n)=2^n+1^n-0^n. G.f. (1-2x^2)/((1-x)(1-2x)). E.g.f. exp(2x)+exp(x)-exp(0).
a(n)=sum{k=0..n, 0^(k(n-k))2^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Feb 09 2005
a(n) = Min{m: A008687(m) = n+1}. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jul 25 2006
Row sums of triangle A132749; = binomial transform of [1, 2, 0, 2, 0, 2, 0, 2,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 28 2007
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EXAMPLE
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------------------------------
n .... a(n) .. a(n) in base 2
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0 ..... 1 ..... 1
1 ..... 3 ..... 11
2 ..... 5 ..... 101
3 ..... 9 ..... 1001
4 .... 17 ..... 10001
5 .... 33 ..... 100001
6 .... 65 ..... 1000001
7 ... 129 ..... 10000001
8 ... 257 ..... 100000001
9 ... 513 ..... 1000000001
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CROSSREFS
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Except for the leading term, the same as A000051. Cf. A083319.
Cf. A132749.
Cf. A000533.
Adjacent sequences: A083315 A083316 A083317 this_sequence A083319 A083320 A083321
Sequence in context: A074858 A074860 A135728 this_sequence A127904 A048578 A087312
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 25 2003
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EXTENSIONS
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Edited by njas, Sep 28 2007
Examples provided by Omar E. Pol (info(AT)polprimos.com), Feb 24 2008.
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