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A087503
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a(n) = 3(a(n-2)+1), with a(0) = 1, a(1) = 3.
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8
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = a(n-1) + A038754(n).
Partial sums of A038754.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..2000
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FORMULA
| a(n)=-(3/2)-(1/3)*(-1)^n*3^[(1/4)*(-1)^n]*3^(1/2)*n*27^(1/4)+(7/6)*3^[(1/4)*(-1)^n]*3^(1/2)*n *27^(1/4), with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 06 2008]
G.f.: g(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.
With a different offset: 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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MAPLE
| 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..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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PROG
| (MAGMA)[(3/2)*(3^Floor(n/2)+3^Floor((n-1)/2)-3^Floor((n-2)/2)-1): n in [1..40]]; // Vincenzo Librandi, Aug 16 2011
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CROSSREFS
| Sequences with similar recurrence rules: A027383(p=2), A133628(p=4), A133629(p=5).
Other related sequences for different p: A016116(p=2), A038754(p=3), A084221(p=4), A133632(p=5).
See A133629 for general formulas with respect to the recurrence rule parameter p.
Related sequences: A132666, A132667, A132668, A132669.
Sequence in context: A128128 A162920 A006330 * A092176 A000991 A095093
Adjacent sequences: A087500 A087501 A087502 * A087504 A087505 A087506
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 11 2003
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EXTENSIONS
| Additional comments from Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 19 2007
Edited by N. J. A. Sloane, May 04 2010. I merged two essentially identical entries with different offsets, so some of the formulas may need to be adjusted.
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