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Search: id:A092055
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| 1, 4, 20, 120, 816, 5984, 45760, 357760, 2829056, 22500864, 179481600, 1433753600, 11461636096, 91659526144, 733141975040, 5864598896640, 46914643623936, 375308558925824, 3002434111406080, 24019335451770880, 192154133857304576
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)= sum_{i=1...(2^n)} i*(i+1)/2, this sequence is thus similar to A016131 as it is a sum of triangular numbers on the interval <1,2^n>, A016131 is a sum of triangular numbers on the interval <1,2^n - 1> [From Ctibor O. Zizka (c.zizka(AT)email.cz), Mar 03 2009]
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FORMULA
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a(n) =(2^(3n-1) +3*2^(2n-1) + 2^n)/3 =A092056(3, n) =A007581(n)*A000079(n) =2*a(n-1)+4^(n-1)+8^(n-1).
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EXAMPLE
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a(5) = C(2+2^5,3) = C(34,3) = 5984
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MAPLE
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seq(-binomial(-2^n, 3), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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CROSSREFS
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Cf. A016131 [From Ctibor O. Zizka (c.zizka(AT)email.cz), Mar 03 2009]
Sequence in context: A089498 A046729 A093123 this_sequence A001715 A020028 A020118
Adjacent sequences: A092052 A092053 A092054 this_sequence A092056 A092057 A092058
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Feb 19 2004
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