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A174513 G.f. satisfies: A(x) = A(x^2)^2 + x*A(x^2)^4. 2
1, 1, 2, 4, 5, 14, 12, 44, 22, 117, 54, 316, 88, 756, 208, 1836, 317, 4126, 690, 9216, 1098, 19906, 2160, 41876, 3556, 87448, 6226, 175832, 11088, 356368, 17232, 693356, 32990, 1365733, 45402, 2593576, 94821, 4971646, 115464, 9271456, 263226 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..4099

FORMULA

A series quadrisection of A(x) equals 2*x^2*A(x^4)^6.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 5*x^4 + 14*x^5 + 12*x^6 +...

A(x)^2 = 1 + 2*x + 5*x^2 + 12*x^3 + 22*x^4 + 54*x^5 + 88*x^6 +...

A(x)^3 = 1 + 3*x + 9*x^2 + 25*x^3 + 57*x^4 + 144*x^5 + 299*x^6 +...

A(x)^4 = 1 + 4*x + 14*x^2 + 44*x^3 + 117*x^4 + 316*x^5 + 756*x^6 +...

A(x)^6 = 1 + 6*x + 27*x^2 + 104*x^3 + 345*x^4 + 1080*x^5 + 3113*x^6 +...

A(x)^8 = 1 + 8*x + 44*x^2 + 200*x^3 + 782*x^4 + 2800*x^5 + 9252*x^6 +...

where the series bisections of A(x)^2 are:

[A(x)^2 - A(-x)^2]/2 = 2*x*A(x^2)^6 and

[A(x)^2 + A(-x)^2]/2 = A(x^2)^4 + x^2*A(x^2)^8.

The series bisections of A(x)^3 are:

[A(x)^3 - A(-x)^3]/2 = 3*x*A(x^2)^8 + x^3*A(x^2)^12 and

[A(x)^3 + A(-x)^3]/2 = A(x^2)^6 + 3*x^2*A(x^2)^10.

The series bisections of A(x)^4 are:

[A(x)^4 - A(-x)^4]/2 = 4*x*A(x^2)^10 + 4*x^3*A(x^2)^14 and

[A(x)^4 + A(-x)^4]/2 = A(x^2)^8 + 6*x^2*A(x^2)^12 + x^4*A(x^2)^16.

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=subst(A, x, x^2+x*O(x^n))^2+x*subst(A, x, x^2+x*O(x^n))^4); polcoeff(A, n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A174512.

Sequence in context: A136563 A127077 A104549 * A000063 A039574 A182375

Adjacent sequences:  A174510 A174511 A174512 * A174514 A174515 A174516

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 20 2010

EXTENSIONS

Edited by Paul D. Hanna, Apr 22 2010

STATUS

approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)