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A105637
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a(n)=a(n-2)+a(n-3)-a(n-5).
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1
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0, 1, 2, 1, 3, 3, 3, 4, 5, 4, 6, 6, 6, 7, 8, 7, 9, 9, 9, 10, 11, 10, 12, 12, 12, 13, 14, 13, 15, 15, 15, 16, 17, 16, 18, 18, 18, 19, 20, 19, 21, 21, 21, 22, 23, 22, 24, 24, 24, 25, 26, 25, 27, 27, 27, 28, 29, 28, 30, 30, 30, 31, 32, 31, 33, 33, 33, 34, 35, 34, 36, 36, 36, 37, 38, 37
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n+6) = a(n) + 3; convolution of A000035(n) with A010872(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 08 2009]
Let B be the periodic sequence that repeats (1,2,1,3,3,3,4,5,4,6,6,6). Then the sequence a(1), a(2),... is obtained by adding 6*(i-1) to every term of the i-th period of B.. - Vladimir Shevelev, May 31 2011
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (0,1,1,0,-1).
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FORMULA
| G.f.: x*(1+2*x)/((1-x^2)*(1-x^3)); a(n)=sum{k=0..n, mod(k, 3)*(1-(-1)^(n+k-1))/2}; a(n)=sum{k=0..floor(n/2), mod(n-2k, 3)}.
a(n) = 1+floor(n/2)-[3 divides n]. - Ralf Stephan, Nov 15 2010.
a(n) = A103221(n-1)+2*A103221(n-2). - R. J. Mathar, Jun 30 2011
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PROG
| (PARI) a(n)=1+floor(n/2)-if(n%3==0, 1, 0)
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CROSSREFS
| Cf. A174257. - Vladimir Shevelev, May 31 2011
Sequence in context: A085599 A110425 A174257 * A029161 A035384 A153868
Adjacent sequences: A105634 A105635 A105636 * A105638 A105639 A105640
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
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