A193377 Real part of g.f. C(x) that satisfies: C(x) = 1 + x*C(I*x)^2.

1, 1, 0, -1, -4, -14, 8, 35, 44, 246, 168, -1906, 296, -5692, -19440, 89539, -104836, 110062, 946856, -3306758, 8516696, 3998844, -36402256, 82221230, -492938376, -657397540, 1092399120, 553666748, 22487269712, 48307873544, -8248804576, -259354056349, -754908556068

Offset

0,5

Links

Table of n, a(n) for n=0..32.

Example

G.f.: C(x) = 1 + x + 2*I*x^2 + (-1 - 4*I)*x^3 + (-4 + 2*I)*x^4 + (-14 - 4*I)*x^5 + (8 - 20*I)*x^6 + (35 + 56*I)*x^7 + (44 - 126*I)*x^8 + (246 - 4*I)*x^9 + (168 + 308*I)*x^10 +...
where
C(x)^2 = 1 + 2*x + (1 + 4*I)*x^2 + (-2 - 4*I)*x^3 + (-14 - 4*I)*x^4 + (-20 - 8*I)*x^5 + (-35 - 56*I)*x^6 + (126 + 44*I)*x^7 + (246 - 4*I)*x^8 +...
The real part of the g.f. begins:
real(C(x)) = 1 + x - x^3 - 4*x^4 - 14*x^5 + 8*x^6 + 35*x^7 + 44*x^8 + 246*x^9 + 168*x^10 - 1906*x^11 + 296*x^12 +...
The imaginary part of the g.f. begins:
imag(C(x)) = 2*x^2 - 4*x^3 + 2*x^4 - 4*x^5 - 20*x^6 + 56*x^7 - 126*x^8 - 4*x^9 + 308*x^10 - 696*x^11 + 5444*x^12 +...

Prog

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

Crossrefs

Cf. A193378 (imag), A193379 (norm).

Sequence in context: A133856 A018853 A218257 * A202731 A098363 A276703

Adjacent sequences: A193374 A193375 A193376 * A193378 A193379 A193380

Keyword

sign

Author

Paul D. Hanna, Jul 24 2011

Status

approved