A143646 Catalan transform of the 3-Fibonacci sequence A006190.

0, 1, 4, 18, 83, 387, 1815, 8541, 40276, 190182, 898844, 4250780, 20111394, 95181166, 450565602, 2133227418, 10101126723, 47834649675, 226540406571, 1072931019393, 5081776592061, 24069823974879, 114009427284309

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Paul Barry, A Catalan Transform and Related Transformations of Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Sergio Falcón and Ángel Plaza, On the Fibonacci k-numbers, Chaos, Solitons & Fractals 2007; 32(5): 1615-24.

Sergio Falcón and Ángel Plaza, The k-Fibonacci sequence and the Pascal 2-triangle Chaos, Solitons & Fractals 2007; 33(1): 38-49.

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*A006130(k-1) with A006130(-1) = 0. - Philippe Deléham, Nov 01 2008

For n>0, a(n) = sum_{k=0..n} (k/n)*C(2n-k-1,n-k)*A006190(k). - Tom Edgar, Mar 09 2014

Prog

(Sage)
q=50 #change q for more terms
[0]+[sum((k/n)*binomial(2*n-k-1, n-k)*lucas_number1(k, 3, -1) for k in [0..n]) for n in [1..q]] # Tom Edgar, Mar 09 2014

Crossrefs

Cf. A006190, A143464.

Sequence in context: A129160 A187077 A218986 * A290916 A014348 A126020

Adjacent sequences: A143643 A143644 A143645 * A143647 A143648 A143649

Keyword

nonn

Author

Sergio Falcon, Oct 27 2008

Status

approved