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A153284
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a(n) = n + Sum_{j=1..n-1} (-1)^j * a(j) for n >= 2, a(1) = 1.
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6
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1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1
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OFFSET
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1,3
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COMMENTS
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Row sums of triangle A153860. - Gary W. Adamson, Jan 03 2009
1 followed by interleaving of A000012 and A010701. - Klaus Brockhaus, Jan 04 2009
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LINKS
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Table of n, a(n) for n=1..70.
Index entries for linear recurrences with constant coefficients, signature (0,1).
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FORMULA
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a(n)=1 if n is 1 or even; a(n)=3 if n is odd other than 1.
G.f.: x*(1 + x + 2*x^2)/((1+x)*(1-x)). - Klaus Brockhaus, Jan 04 2009 and Oct 15 2009
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EXAMPLE
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a(1)=1, a(2)=2-a(1)=2-1=1, a(3)=3+a(2)-a(1)=3+1-1=3, a(4)=4-a(3)+a(2)-a(1)=4-3+1-1=1, a(5)=5+1-3+1-1=3, a(6)=6-3+1-3+1-1=1, a(7)=7+1-3+1-3+1-1, etc.
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PROG
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(MAGMA) S:=[ 1 ]; for n in [2..105] do Append(~S, n + &+[ (-1)^j*S[j]: j in [1..n-1] ]); end for; S; // Klaus Brockhaus, Jan 04 2009
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CROSSREFS
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Equals A010684 with the addition of the leading term of 1
The first sequence of a family that includes A153285 and A153286
Cf. A153860.
Cf. A000012 (all 1's sequence), A010701 (all 3's sequence). - Klaus Brockhaus, Jan 04 2009
Sequence in context: A277109 A063062 A066056 * A112030 A010684 A176040
Adjacent sequences: A153281 A153282 A153283 * A153285 A153286 A153287
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KEYWORD
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easy,nonn
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AUTHOR
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Walter Carlini, Dec 23 2008
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STATUS
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approved
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