A112570 G.f. A(x) satisfies: A(x)^2 equals the g.f. of A110630, which consists entirely of numbers 1 through 4.

1, 1, 1, 1, -1, 2, 0, 1, -2, 5, -5, 4, -6, 18, -30, 35, -43, 84, -167, 261, -352, 545, -1010, 1790, -2783, 4207, -7025, 12464, -21071, 33567, -54154, 92317, -159366, 266150, -435285, 725260, -1239404, 2112351, -3535532, 5894852, -9964767, 17008752, -28880694, 48645873

Offset

0,6

Comments

A110630 is formed from every 2nd term of A083954, which also consists entirely of numbers 1 through 4.

Links

Table of n, a(n) for n=0..43.

Formula

G.f. A(x) satisfies: A(x)^4 (mod 8) = g.f. of A083954.

Example

A(x) = 1 + x + x^2 + x^3 - x^4 + 2*x^5 + x^7 - 2*x^8 + 5*x^9 +...
A(x)^2 = 1 + 2*x + 3*x^2 + 4*x^3 + x^4 + 4*x^5 + 3*x^6 +...
A(x)^4 = 1 + 4*x + 10*x^2 + 20*x^3 + 27*x^4 + 36*x^5 +...
A(x)^4 (mod 8) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...
G(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 + 4*x^6 +...
where G(x) is the g.f. of A083954.

Prog

(PARI) {a(n)=local(d=2, m=4, A=1+m*x); for(j=2, d*n, for(k=1, m, t=polcoeff((A+k*x^j+x*O(x^j))^(1/m), j); if(denominator(t)==1, A=A+k*x^j; break))); polcoeff(Ser(vector(n+1, i, polcoeff(A, d*(i-1))))^(1/2), n)}

Crossrefs

Cf. A110630, A083954.

Sequence in context: A055509 A334226 A006667 * A127755 A180662 A318144

Adjacent sequences: A112567 A112568 A112569 * A112571 A112572 A112573

Keyword

sign

Author

Paul D. Hanna, Sep 14 2005

Status

approved