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Search: id:A133628
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| A133628 |
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a(1)=1, a(n)=a(n-1)+(p-1)*p^(n/2-1) if n is even, else a(n)=a(n-1)+p^((n-1)/2), where p=4. |
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7
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| 1, 4, 8, 20, 36, 84, 148, 340, 596, 1364, 2388, 5460, 9556, 21844, 38228, 87380, 152916, 349524, 611668, 1398100, 2446676, 5592404, 9786708, 22369620, 39146836, 89478484, 156587348, 357913940, 626349396, 1431655764, 2505397588
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Partial sums of A084221.
This is essentially a duplicate of A097164. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2008
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FORMULA
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a(n)=sum{1<=k<=n, A084221(k)}.
G.f.: g(x)=x(1+3x)/((1-4x^2)(1-x)).
a(n)=(4/3)*(4^(n/2)-1) if n is even, else a(n)=(4/3)*(7*4^((n-3)/2)-1).
a(n)=(4/3)*(4^floor(n/2)+4^floor((n-1)/2)-4^floor((n-2)/2)-1).
a(n)=4^floor(n/2)+4^floor((n+1)/2)/3-4/3.
a(n)=A132668(a(n+1))-1.
a(n)=A132668(a(n-1)+1) for n>0.
A132668(a(n))=a(n-1)+1 for n>0.
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=4*a[n-2]+4 od: seq(a[n], n=1..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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CROSSREFS
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Sequences with similar recurrence rules: A027383(p=2), A133627(p=3), A133629(p=5).
See A133629 for general formulas with respect to the recurrence rule parameter p.
Related sequences: A132666, A132667, A132668, A132669.
Other related sequences for different p: A016116(p=2), A133626(p=3), A084221(p=4), A133632(p=5).
Sequence in context: A152233 A053303 A097164 this_sequence A097940 A032280 A156303
Adjacent sequences: A133625 A133626 A133627 this_sequence A133629 A133630 A133631
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 19 2007
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