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 A143464 Catalan transform of the Pell sequence. 4
 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; text; internal format)
 OFFSET 0,3 LINKS Paul Barry, A Catalan Transform and Related Transformations of Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4 Paul Barry and Aoife Hennessy, Generalized Narayana Polynomials, Riordan Arrays, and Lattice Paths, Journal of Integer Sequences, Vol. 15, 2012, #12.4.8. - From N. J. A. Sloane, Oct 08 2012 Sergio Falcon, Catalan transform of the K-Fibonacci sequence, Commun. Korean Math. Soc. 28 (2013), No. 4, pp. 827-832; http://dx.doi.org/10.4134/CKMS.2013.28.4.827. Sergio Falcon and Ángel Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solitons & Fractals 2007; 33(1): 38-49. Sergio Falcon and Ángel Plaza, On the Fibonacci k-numbers, Chaos, Solitons & Fractals 2007; 32(5): 1615-24. 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). - Philippe Deléham, Oct 28 2008 a(n)=Sum_{k, 0<=k<=n} A039599(n,k)*A000035(k)*A016116(k). - Philippe Deléham, Oct 28 2008 G.f.: (1-5*x-(1+x)*sqrt(1-4*x))/(2*x^2+16*x-4). - Mark van Hoeij, May 01 2013 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}] PROG (PARI) x='x+O('x^66); concat([0], Vec((1-5*x-(1+x)*sqrt(1-4*x))/(2*x^2+16*x-4))) \\ Joerg Arndt, May 01 2013 CROSSREFS Cf. A109262, A000129. Sequence in context: A122368 A032443 A180907 * A270561 A259858 A117641 Adjacent sequences:  A143461 A143462 A143463 * A143465 A143466 A143467 KEYWORD nonn AUTHOR Sergio Falcon, Oct 24 2008 EXTENSIONS Offset corrected by Philippe Deléham, Oct 28 2008 STATUS approved

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Last modified August 18 08:42 EDT 2018. Contains 313823 sequences. (Running on oeis4.)