A223142 G.f. satisfies: A(x)^2 = A(x^2)^2 + 4*x.

1, 2, 0, 0, 2, -4, 8, -16, 32, -56, 88, -112, 64, 240, -1264, 4064, -10814, 25500, -54200, 102832, -166020, 190808, 22304, -1058880, 4412424, -13496544, 35306480, -82326496, 172081840, -315115328, 464910368, -363016000, -871587808, 5713552456, -20289991016

Offset: 0

Author

Paul D. Hanna, Mar 15 2013

Keywords

• sign

Examples

			G.f.: A(x) = 1 + 2*x + 2*x^4 - 4*x^5 + 8*x^6 - 16*x^7 + 32*x^8 - 56*x^9 +...
where
A(x)^2 = 1 + 4*x + 4*x^2 + 4*x^4 + 4*x^8 + 4*x^16 + 4*x^32 +...+ 4*x^(2^n) +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A223143, A107086, A223026.

Programs

PARI

{a(n)=local(A=1+x); for(i=1,#binary(n), A=(subst(A, x, x^2)^2+4*x+x*O(x^n))^(1/2)); polcoeff(A, n, x)}
for(n=0,40,print1(a(n),", "))

Formula

G.f.: A(x) = sqrt( 1 + Sum_{n>=0} 4*x^(2^n) ).