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A143464
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Catalan transform of the Pell sequence.
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5
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0, 1, 3, 11, 42, 164, 649, 2591, 10408, 41998, 170050, 690370, 2808714, 11446642, 46715469, 190876527, 780679200, 3195628806, 13090353594, 53655587034, 220045073988, 902842397664, 3705876933930, 15216954519222, 62503485455208
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Barry, P. A Catalan Transform and Related Transformations of Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4
Falcon S. and Plaza \'A. The $k$-Fibonacci sequence and the Pascal $2$-triangle. Chaos, Solitons \& Fractals 2007; 33(1): 38-49.
Falcon S. and Plaza \'A. On the Fibonacci $k$-numbers. Chaos, Solitons \& Fractals 2007; 32(5): 1615-24.
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FORMULA
| CF_{2,0}:=0 CF_{2,n}:= sum_{i=0}^n frac{i}{2n-i} {{2n-i}choose{n-i}} Fibonacci[n,k] for n>=1
a(n)=Sum_{k, 0<=k<=n} A106566(n,k)*A000129(k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008]
a(n)=Sum_{k, 0<=k<=n} A039599(n,k)*A000035(k)*A016116(k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008]
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MATHEMATICA
| Clear["Global`"] f[n_, k_] := Fibonacci[n, k] n = 25; k = 2; Do[Print[Sum[i/(2j - i) Binomial[2j - i, j - i]*f[i, k], {i, 0, j}]], {j, 1, n}]
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CROSSREFS
| Cf. A109262, A000129.
Sequence in context: A122368 A032443 A180907 * A117641 A200030 A084782
Adjacent sequences: A143461 A143462 A143463 * A143465 A143466 A143467
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KEYWORD
| nonn
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AUTHOR
| Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Oct 24 2008
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EXTENSIONS
| Corrected offset. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008
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