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Search: id:A054451
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| 1, 1, 4, 5, 12, 17, 33, 50, 88, 138, 232, 370, 609, 979, 1596, 2575, 4180, 6755, 10945, 17700, 28656, 46356, 75024, 121380, 196417, 317797, 514228, 832025, 1346268, 2178293, 3524577, 5702870, 9227464, 14930334, 24157816, 39088150, 63245985
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OFFSET
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0,3
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FORMULA
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a(n)= A054450(n+2, 2). G.f.: Fib(x)/(1-x^2)^2, with Fib(x)=1/(1-x-x^2) = g.f. A000045 (Fibonacci numbers without 0).
a(2*k)= A027941(k)= F(2*k+3)-1; a(2*k+1)= F(2*(k+2))-(k+2)= A054452(k), k >= 0.
a(n-2)=Fibonacci(n+1)-binomial(n-floor(n/2), floor(n/2)), or a(n-2)=sum(i=0, floor(n/2)-1, binomial(n-i, i)) - Jon Perry (perry(AT)globalnet.co.uk), Mar 18 2004
a(n)=sum{k=0..floor(n/2), binomial(n-k+2, k)}. - Paul Barry (pbarry(AT)wit.ie), Oct 23 2004
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MAPLE
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BB:=k^2/(1-k^2)^2/(1-k-k^2): BBser:=series(BB, k=0, 43): seq(coeff(BBser, k, n), n=2..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2007
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CROSSREFS
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Cf. A054450, A049310, A000045, A052952.
Cf. A007382.
Adjacent sequences: A054448 A054449 A054450 this_sequence A054452 A054453 A054454
Sequence in context: A103650 A131116 A131328 this_sequence A123102 A028272 A003969
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 27 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 28 2000
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