A174513 G.f. satisfies: A(x) = A(x^2)^2 + x*A(x^2)^4.

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

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: A127077 A367027 A104549 * A000063 A368378 A367298

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