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Search: id:A084214
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| A084214 |
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Inverse binomial transform of a math magic problem. |
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+0
6
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| 1, 1, 4, 6, 14, 26, 54, 106, 214, 426, 854, 1706, 3414, 6826, 13654, 27306, 54614, 109226, 218454, 436906, 873814, 1747626, 3495254, 6990506, 13981014, 27962026, 55924054, 111848106, 223696214, 447392426, 894784854, 1789569706, 3579139414
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Inverse binomial transform of A060816.
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FORMULA
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a(n)=(5*2^n-3*0^n+4(-1)^n)/6; G.f.: (1+x^2)/((1+x)(1-2x)); E.g.f.: (5exp(2x)-3exp(0)+4exp(-x))/6.
The binomial transform of A084214(n+1) is A020989(n). a(n)=A001045(n-1)+A001045(n+1)-0^n/2. - Paul Barry (pbarry(AT)wit.ie), May 04 2004
a(n)=sum{k=0..n, A001045(n+1)C(1, k/2)(1+(-1)^k)/2} - Paul Barry (pbarry(AT)wit.ie), Oct 15 2004
a(n) = a(n-1)+2*a(n-2) for n > 2; a(0) = 1, a(1) = 1, a(2) = 4. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 01 2009]
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MAPLE
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a[0]:=1:a[1]:=4:for n from 2 to 50 do a[n]:=a[n-1]+2*a[n-2]od: seq(a[n], n=-1..31); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 15 2008]
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CROSSREFS
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Sequence in context: A097271 A126867 A027632 this_sequence A030138 A009849 A103419
Adjacent sequences: A084211 A084212 A084213 this_sequence A084215 A084216 A084217
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KEYWORD
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easy,nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 19 2003
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