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A143646 Catalan transform of the 3-Fibonacci sequence A006190. 1
0, 1, 4, 18, 83, 387, 1815, 8541, 40276, 190182, 898844, 4250780, 20111394, 95181166, 450565602, 2133227418, 10101126723, 47834649675, 226540406571, 1072931019393, 5081776592061, 24069823974879, 114009427284309 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 24 04:33 EST 2018. Contains 299595 sequences. (Running on oeis4.)