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A074662
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a(n) = F(n+1)+cos(n*pi/2).
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2
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2, 1, 1, 3, 6, 8, 12, 21, 35, 55, 88, 144, 234, 377, 609, 987, 1598, 2584, 4180, 6765, 10947, 17711, 28656, 46368, 75026, 121393, 196417, 317811, 514230, 832040, 1346268, 2178309, 3524579, 5702887, 9227464, 14930352, 24157818, 39088169
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) is the convolution of L(n) with the sequence (1,0,-1,0,1,0,-1,0,....) A056594. a(2n+1)=F(2n+2), F = Fibonacci numbers.
a(n)=Sum((-1)^(i+Floor(n/2))L(2i+e),(i=0,..,Floor(n/2))), where L(n) Lucas numbers and e=(1/2)(1-(-1)^n).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,1,1)
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FORMULA
| a(n)=a(n-1)+a(n-3)+a(n-4), a(0)=2, a(1)=1, a(2)=1, a(3)=3. G.f.: (2 - x)/(1 - x - x^3 - x^4).
a(4n)=F(4n+1)+1, a(4n+2)=F(4n+3)-1.
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MATHEMATICA
| CoefficientList[Series[(2 - x)/(1 - x - x^3 - x^4), {x, 0, 40}], x]
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PROG
| (PARI) a(n)=if(n<0, 0, fibonacci(n+1)+real(I^n))
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CROSSREFS
| Cf. A056594.
Sequence in context: A136462 A060517 A163181 * A025243 A144512 A159314
Adjacent sequences: A074659 A074660 A074661 * A074663 A074664 A074665
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Aug 29 2002
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