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A283679 G.f.: F(F(F(x))) where F(x) = x/(1-x-x^2) is the g.f. for the Fibonacci numbers.Three fold self composition of the Fibonacci generating series x/(1-x-x^2) in A000045. 2
0, 1, 3, 12, 48, 197, 815, 3391, 14153, 59185, 247791, 1038186, 4351706, 18245861, 76514483, 320899470, 1345931153, 5645394769, 23679726926, 99326654214, 416638208001, 1747652017025, 7330817809523, 30750407615699 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Three-fold self composition of the Fibonacci generating series x/(1-x-x^2).

Composition in either order of A000045 and A270863.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f. = -(x^2+x-1)*x*(x^4+3*x^3-x^2-3*x+1)/(x^8+7*x^7+10*x^6-13*x^5-21*x^4+13*x^3+10*x^2-7*x+1).

Recurrence:

a(0)=0, a(1)=1, a(2)=3, a(3)=14, a(4)=60, a(5)=259, a(6)= 1103, a(7)=4673; thereafter

a(k) = 7*a(k-1)-10*a(k-2)-13*a(k-3)+21*a(k-4)+13*a(k-5)-10*a(k-6)-7*a(k-7)-a(k-8) for k >7.

MAPLE

f:= x-> x/(1-x-x^2):

a:= n-> coeff(series(f(f(f(x))), x, n+1), x, n):

seq(a(n), n=0..23);

CROSSREFS

Sequence in context: A113956 A323261 A103943 * A165328 A142873 A301578

Adjacent sequences:  A283676 A283677 A283678 * A283680 A283681 A283682

KEYWORD

nonn

AUTHOR

Oboifeng Dira, Mar 14 2017

EXTENSIONS

Edited by N. J. A. Sloane, Apr 21 2017

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)