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A052959
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a(2n) = a(2n-1)+a(2n-2), a(2n+1) = a(2n)+a(2n-1)-1, a(0)=2, a(1)=1.
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1
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2, 1, 3, 3, 6, 8, 14, 21, 35, 55, 90, 144, 234, 377, 611, 987, 1598, 2584, 4182, 6765, 10947, 17711, 28658, 46368, 75026, 121393, 196419, 317811, 514230, 832040, 1346270, 2178309, 3524579, 5702887, 9227466, 14930352, 24157818, 39088169
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1030
Index to sequences with linear recurrences with constant coefficients, signature (1,2,-1,-1).
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FORMULA
| G.f.: -(-2+x+2*x^2)/(-1+x+x^2)/(-1+x^2)
Recurrence: {a(1)=1, a(2)=3, a(0)=2, -a(n)-2*a(n+1)+1+a(n+3)}
Sum(1/5*(1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^2))+Sum(1/2*_alpha^(-n), _alpha=RootOf(-1+_Z^2))
a(n) = Fibonacci(n+1)+(1+(-1)^n)/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 23 2003
a(n)=sum{k=0..n, C(k, n-k)+(-1)^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Jul 21 2003
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MAPLE
| spec := [S, {S=Union(Sequence(Union(Prod(Z, Z), Z)), Sequence(Prod(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
| Sequence in context: A108949 A167704 * A109522 A034399 A005292 A183256
Adjacent sequences: A052956 A052957 A052958 * A052960 A052961 A052962
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000
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