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A186576 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^[n*phi] where phi = (1+sqrt(5))/2. 3
1, 1, 2, 6, 20, 72, 274, 1083, 4402, 18283, 77248, 330966, 1434527, 6278831, 27712795, 123203934, 551208007, 2479863162, 11212189575, 50918544674, 232161960449, 1062356169341, 4877198070463, 22457825237584, 103693977154771 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

FORMULA

G.f. satisfies: A(x) = G(x/A(x)) where A(x*G(x)) = G(x) is the g.f. of A186577, which in turn satisfies: G(x) = Sum_{n>=0} x^n*G(x)^[n*phi^2].

G.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) is the g.f. of A186577.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 72*x^5 + 274*x^6 +...

The g.f. satisfies:

A(x) = 1 + x*A(x) + x^2*A(x)^3 + x^3*A(x)^4 + x^4*A(x)^6 + x^5*A(x)^8 + x^6*A(x)^9 + x^7*A(x)^11 +...+ x^n*A(x)^A000201(n) +...

The g.f. of A186577, G(x) = A(x*G(x)), satisfies:

G(x) = 1 + x*G(x)^2 + x^2*G(x)^5 + x^3*G(x)^7 + x^4*G(x)^10 + x^5*G(x)^13 + x^6*G(x)^15 + x^7*G(x)^18 +...+ x^n*G(x)^A001950(n) +...

and begins:

G(x) = 1 + x + 3*x^2 + 13*x^3 + 65*x^4 + 353*x^5 + 2025*x^6 +...

Since A(x) = G(x/A(x)), then:

A(x) = 1 + x/A(x) + 3*x^2/A(x)^2 + 13*x^3/A(x)^3 + 65*x^4/A(x)^4 +...

PROG

(PARI) {a(n)=local(A=1+x, phi=(1+sqrt(5))/2); for(i=1, n, A=sum(m=0, n, x^m*(A+x*O(x^n))^floor(m*phi))); polcoeff(A, n)}

CROSSREFS

Cf. A186577, A000201 (lower Wythoff sequence).

Sequence in context: A071356 A141200 A186996 * A272485 A122737 A150134

Adjacent sequences:  A186573 A186574 A186575 * A186577 A186578 A186579

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 24 2011

STATUS

approved

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Last modified November 19 12:38 EST 2018. Contains 317351 sequences. (Running on oeis4.)