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Search: id:A133627
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| A133627 |
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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=3. |
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+0
9
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| 1, 3, 6, 12, 21, 39, 66, 120, 201, 363, 606, 1092, 1821, 3279, 5466, 9840, 16401, 29523, 49206, 88572, 147621, 265719, 442866, 797160, 1328601, 2391483, 3985806, 7174452, 11957421, 21523359, 35872266, 64570080, 107616801, 193710243
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OFFSET
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1,2
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COMMENT
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Partial sums of A133626.
This is essentially a duplicate of A087503. - 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, A133626(k)}.
G.f.: g(x)=x(1+2x)/((1-3x^2)(1-x)).
a(n)=(3/2)*(3^(n/2)-1) if n is even, else a(n)=(3/2)*(5*3^((n-3)/2)-1).
a(n)=(3/2)*(3^floor(n/2)+3^floor((n-1)/2)-3^floor((n-2)/2)-1).
a(n)=3^floor(n/2)+3^floor((n+1)/2)/2-3/2.
a(n)=A132667(a(n+1))-1.
a(n)=A132667(a(n-1)+1) for n>0.
A132667(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]:=3*a[n-2]+3 od: seq(a[n], n=1..34); - 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), A133628(p=4), 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: A128128 A006330 A087503 this_sequence A092176 A000991 A095093
Adjacent sequences: A133624 A133625 A133626 this_sequence A133628 A133629 A133630
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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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