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Search: id:A164907
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| A164907 |
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a(n) = (3*3^n-(-1)^n)/2. |
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+0
3
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| 1, 5, 13, 41, 121, 365, 1093, 3281, 9841, 29525, 88573, 265721, 797161, 2391485, 7174453, 21523361, 64570081, 193710245, 581130733, 1743392201, 5230176601, 15690529805, 47071589413, 141214768241, 423644304721, 1270932914165
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Interleaving of A096053 and A083884 without initial term 1.
Partial sums are (essentially) in A080926. First differences are (essentially) in A105723.
a(n)+a(n+1) = A008776(n+1) = A099856(n+1) = A110593(n+2).
Binomial transform of A164906. Inverse binomial transform of A164908.
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FORMULA
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a(n) = 2*a(n-1)+3*a(n-2) for n > 1; a(0) = 1, a(1) = 5.
G.f.: (1+3*x)/((1+x)*(1-3*x)).
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PROGRAM
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(MAGMA) [ (3*3^n-(-1)^n)/2: n in [0..25] ];
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CROSSREFS
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Equals A046717 without initial term 1 and A080925 without initial term 0. Equals A084182 / 2 from second term onward.
Cf. A096053, A083884, A080926, A105723, A008776, A099856, A110593, A164906, A164908.
Sequence in context: A034735 A046717 A080925 this_sequence A085601 A147718 A111009
Adjacent sequences: A164904 A164905 A164906 this_sequence A164908 A164909 A164910
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 31 2009
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