OFFSET
0,1
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1961
Sergio Falcon, Half self-convolution of the k-Fibonacci sequence, Notes on Number Theory and Discrete Mathematics (2020) Vol. 26, No. 3, 96-106.
FORMULA
a(n) = sum(binomial(n,k)*L(k)*L(n-k),k=0..n)/2, n>=0, with L(n)=A000032(n).
E.g.f.: (1/2)*(exp(phi*x)+exp(-(phi-1)*x))^2 =
exp(x)*(cosh(sqrt(5)*x)+1), with the golden section phi:=(1+sqrt(5))/2. (See the e.g.f. of A000032).
a(n) = 2^(n-1)*L(n) + 1.
a(n) = 5*A014335(n) + 2. - Vladimir Reshetnikov, Oct 06 2016
EXAMPLE
With A000032 = {2,1,3,4,7,...},
2*a(4) = 1*2*7 + 4*1*4 + 6*3*3 + 4*4*1 + 1*7*2 = 114.
MATHEMATICA
Array[Sum[Binomial[#, k] LucasL[k] LucasL[# - k], {k, 0, #}]/2 &, 28, 0] (* Michael De Vlieger, Dec 28 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 14 2012
STATUS
approved