A107086 G.f. A(x) satisfies: A(x)^4 = A(x^2)^2 + 4*x.

1, 1, -1, 2, -5, 13, -35, 99, -289, 857, -2578, 7864, -24252, 75430, -236348, 745431, -2364399, 7536482, -24127482, 77544613, -250098478, 809169322, -2625483810, 8541037140, -27851360659, 91018956200, -298052119611, 977825373366, -3213513271929, 10577811289462, -34870732260397

Offset

0,4

Comments

Self-convolution is A107087. Self-convolution 4th power is A107088.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Example

A(x)^4 = 1 + 4*x + 2*x^2 - x^4 + 2*x^6 - 5*x^8 + 12*x^10 - 30*x^12 +...
A(x^2)^2 = 1 + 2*x^2 - x^4 + 2*x^6 - 5*x^8 + 12*x^10 - 30*x^12 +...

Mathematica

nmin = 0; nmax = 30; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x]^4 - A[x^2]^2 - 4x + O[x]^(n+1), x][[2;; ]] == 0 /. sol; sol = sol ~Join~ Solve[eq][[1]], {n, 2, nmax}];
a /@ Range[nmin, nmax] /. sol (* Jean-François Alcover, Nov 07 2019 *)

Prog

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

Crossrefs

Cf. A107087, A107088, A187814, A228711.

Sequence in context: A037247 A308273 A126221 * A294790 A234643 A089846

Adjacent sequences: A107083 A107084 A107085 * A107087 A107088 A107089

Keyword

sign

Author

Paul D. Hanna, May 11 2005

Status

approved