A174512 G.f. satisfies: A(x) = A(x^2)^2 + x*A(x^2)^3.

1, 1, 2, 3, 5, 9, 10, 22, 20, 51, 40, 114, 67, 230, 130, 474, 203, 891, 380, 1725, 575, 3108, 1032, 5718, 1524, 9986, 2600, 17568, 3874, 30048, 6290, 50988, 9420, 85647, 14450, 140796, 22195, 233095, 32260, 373536, 50656, 609804, 69464, 956368

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n), n=0..8200.

Formula

A series quadrisection of A(x) equals 2*x^2*A(x^4)^5.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 9*x^5 + 10*x^6 +...
A(x)^2 = 1 + 2*x + 5*x^2 + 10*x^3 + 20*x^4 + 40*x^5 + 67*x^6 +...
A(x)^3 = 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 114*x^5 + 230*x^6 +...
A(x)^4 = 1 + 4*x + 14*x^2 + 40*x^3 + 105*x^4 + 260*x^5 + 594*x^6 +..
A(x)^5 = 1 + 5*x + 20*x^2 + 65*x^3 + 190*x^4 + 516*x^5 + 1300*x^6 +...
A(x)^6 = 1 + 6*x + 27*x^2 + 98*x^3 + 315*x^4 + 930*x^5 + 2546*x^6 +...
where the series bisections of A(x)^2 are:
[A(x)^2 - A(-x)^2]/2 = 2*x*A(x^2)^5 and
[A(x)^2 + A(-x)^2]/2 = A(x^2)^4 + x^2*A(x^2)^6.
The series bisections of A(x)^3 are:
[A(x)^3 - A(-x)^3]/2 = 3*x*A(x^2)^7 + x^3*A(x^2)^9 and
[A(x)^3 + A(-x)^3]/2 = A(x^2)^6 + 3*x^2*A(x^2)^8.
The series bisections of A(x)^4 are:
[A(x)^4 - A(-x)^4]/2 = 4*x*A(x^2)^9 + 4*x^3*A(x^2)^11 and
[A(x)^4 + A(-x)^4]/2 = A(x^2)^8 + 6*x^2*A(x^2)^10 + x^4*A(x^2)^12.

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))^3); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Cf. A174513.

Sequence in context: A090845 A262990 A058108 * A056144 A284626 A284847

Adjacent sequences: A174509 A174510 A174511 * A174513 A174514 A174515

Keyword

nonn

Author

Paul D. Hanna, Apr 20 2010

Extensions

Edited by Paul D. Hanna, Apr 22 2010

Status

approved