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Search: id:A082761
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| 1, 4, 20, 104, 544, 2848, 14912, 78080, 408832, 2140672, 11208704, 58689536, 307302400, 1609056256, 8425127936, 44114542592, 230986743808, 1209462292480, 6332826779648, 33159111507968, 173623361929216, 909103725543424
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OFFSET
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0,2
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COMMENT
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Hankel transform of sum{k=0..n, (-1)^k*C(2k,k)} (see A054108). [From Paul Barry (pbarry(AT)wit.ie), Jan 13 2009]
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FORMULA
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a(n) = Sum[ Trinomial[n, k] Fibonacci[k+1], {k, 0, 2n} ] where Trinomial[n, k] = trinomial coefficients (A027907)
a(n) = 2^n Fibonacci[2n+1]
Third binomial transform of (1, 1, 5, 5, 25, 25, ....). a(n)=((1+sqrt(5))(3+sqrt(5))^n-(1-sqrt(5))(3-sqrt(5))^n)/(2sqrt(5)). - Paul Barry (pbarry(AT)wit.ie), Jul 16 2003
G.f.: (1-2x)/(1-6x+4x^2). a(n)= 6*a(n-1)-4*a(n-2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 04 2008]
a(n)=Sum_{k, 0<=k<=n}A147703(n,k)*3^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]
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CROSSREFS
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Sequence in context: A105480 A155485 A155181 this_sequence A076035 A120978 A035028
Adjacent sequences: A082758 A082759 A082760 this_sequence A082762 A082763 A082764
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KEYWORD
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easy,nonn
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AUTHOR
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Emanuele Munarini (munarini(AT)mate.polimi.it), May 21 2003
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