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A053602
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a(n)=a(n-1)-(-1)^n*a(n-2), a(0)=0, a(1)=1.
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5
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0, 1, 1, 2, 1, 3, 2, 5, 3, 8, 5, 13, 8, 21, 13, 34, 21, 55, 34, 89, 55, 144, 89, 233, 144, 377, 233, 610, 377, 987, 610, 1597, 987, 2584, 1597, 4181, 2584, 6765, 4181, 10946, 6765, 17711, 10946, 28657, 17711, 46368, 28657, 75025, 46368, 121393, 75025
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OFFSET
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0,4
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COMMENTS
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If b(0)=0, b(1)=1 and b(n)=b(n-1)+(-1)^n*b(n-2), then a(n)=b(n+3) [From Jaume Oliver Lafont, Oct 03 2009]
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REFERENCES
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Krithnaswami Alladi and V. E. Hoggatt, Jr. Compositions with Ones and Twos, Fibonacci Quarterly, 13 (1975), 233-239 [From Ron Knott, Oct 29 2010]
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LINKS
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Table of n, a(n) for n=0..50.
Index entries for two-way infinite sequences
Index to sequences with linear recurrences with constant coefficients, signature (0,1,0,1)
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FORMULA
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G.f.: x*(1+x+x^2)/(1-x^2-x^4). a(n)=a(n-2)+a(n-4).
a(2n)=F(n), a(2n-1)=F(n+1) where F() is Fibonacci sequence.
a(3)=1, a(4)=2, for n>4 a(n+2)=a(n+1)+sign(a(n)-a(n+1))*a(n) - Benoit Cloitre, Apr 08 2002
a(n) = A079977(n-1) + A079977(n-2) + A079977(n-3), n>2. - Ralf Stephan, Apr 26 2003
a(0) = 0, a(1) = 1; a(2n) = a(2n-1)-a(2n-2); a(2n+1) = a(2n) + a(2n-1). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 21 2005
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PROG
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(PARI) a(n)=fibonacci(n\2+n%2*2)
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CROSSREFS
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a(3-n)=A051792(n). Cf. A000045.
Sequence in context: A114209 A132091 A051792 * A123231 A058736 A097451
Adjacent sequences: A053599 A053600 A053601 * A053603 A053604 A053605
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Jan 17 2000
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STATUS
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approved
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