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A279277
Composition of Lucas numbers A000032 with Fibonacci numbers A000045.
0
1, 4, 12, 37, 110, 327, 968, 2864, 8469, 25040, 74029, 218856, 647008, 1912753, 5654670, 16716883, 49420052, 146100276, 431915561, 1276869920, 3774804441, 11159436284, 32990587972, 97529916957, 288327225550, 852380393407, 2519888066928, 7449533000584, 22023018662909
OFFSET
1,2
COMMENTS
G(F(x)) where F(x) = x+x^2+2x^3+3x^4+... is the generating series of the Fibonacci numbers A000045 and G(x) = x+3x^2+4x^3+7x^4 +... is the generating series of the Lucas numbers A000032.
FORMULA
G.f. x*(1+x-x^2)/(1-3*x-x^2+3*x^3+x^4).
a(n) = 3*a(n-1)+a(n-2)-3*a(n-3)-a(n-4), a(1)=1, a(2)=4, a(3)=12, a(4)=46.
EXAMPLE
(x+x^2)/(1-3x) = x + (3+1)x^2+... so a(1) = 1 and a(2) = 4.
MATHEMATICA
Rest@ CoefficientList[Series[(x + x^2 - x^3)/(1 - 3 x - x^2 + 3 x^3 + x^4), {x, 0, 24}], x] (* Michael De Vlieger, Dec 12 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Oboifeng Dira, Dec 10 2016
STATUS
approved