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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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6
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is essentially a duplicate of A097164. - R. J. Mathar, Jun 08 2008
Partial sums of A084221.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..3000
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FORMULA
| a(n) = sum(k=1..n, A084221(k) ).
G.f.: x*(1+3*x)/((1-4*x^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
| 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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PROG
| (MAGMA) [4^Floor(n/2)+4^Floor((n+1)/2)/3-4/3: n in [1..40]]; // Vincenzo Librandi, Aug 17 2011
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CROSSREFS
| Sequences with similar recurrence rules: A027383(p=2), A087503(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), A038754(p=3), A084221(p=4), A133632(p=5).
Sequence in context: A152233 A053303 A097164 * A097940 A032280 A156303
Adjacent sequences: A133625 A133626 A133627 * A133629 A133630 A133631
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KEYWORD
| nonn
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 19 2007
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