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A074331
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a(n) = F(n+1)-(1+(-1)^n)/2.
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9
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0, 1, 1, 3, 4, 8, 12, 21, 33, 55, 88, 144, 232, 377, 609, 987, 1596, 2584, 4180, 6765, 10945, 17711, 28656, 46368, 75024, 121393, 196417, 317811, 514228, 832040, 1346268, 2178309, 3524577, 5702887, 9227464, 14930352, 24157816, 39088169
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) is the convolution of F(n) with the sequence (1,0,1,0,1,0,...)
Transform of F(n) under the Riordan array (1/(1-x^2),x). - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,2,-1,-1)
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FORMULA
| a(n)= Sum (F(2i+e),(i=0,1,..,Floor(n/2))), where F(n) are Fibonacci numbers and e=2(n/2 - Floor(n/2)).
a(n)=a(n-1)+2a(n-2)-a(n-3)-a(n-4), a(0)=0, a(1)=1, a(2)=1, a(3)=3.
G.f.: x / ( (x-1)*(1+x)*(x^2+x-1) )
a(2n+1)=F(2n+2), a(2n)=F(2n+1)-1.
a(n-1)=sum{k=0..floor(n/2), binomial(n-k, k-1)} - Paul Barry (pbarry(AT)wit.ie), Jul 07 2004
a(n)=sum{k=0..floor((n-1)/2), F(n-2k)}; - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
a(n)=sum{k=0..n, F(k)*(1-(-1)^floor((n+k-1)/2))}; - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
a(n) =fibonacci(n-1)+a(n-2), a(2)=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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MAPLE
| with (combinat):a[2]:=1:for n from 2 to 50 do a[n]:=fibonacci(n-1)+a[n-2] od: seq(a[n], n=1..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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MATHEMATICA
| CoefficientList[Series[x/(1-x-2*x^2+x^3+x^4), {x, 0, 40}], x]
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PROG
| (PARI) a(n)=if(n<0, 0, fibonacci(n+1)-(n+1)%2)
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CROSSREFS
| Essentially the same as A052952.
Sequence in context: A147622 A173534 A052952 * A153339 A033955 A049720
Adjacent sequences: A074328 A074329 A074330 * A074332 A074333 A074334
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Aug 21 2002
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