A112572 G.f. A(x) satisfies: A(x)^4 equals the g.f. of A110638, which consists entirely of numbers 1 through 8.

1, 1, -1, 3, -6, 18, -52, 156, -481, 1512, -4828, 15621, -51081, 168537, -560309, 1874975, -6309964, 21341241, -72497698, 247247463, -846187023, 2905210526, -10003144986, 34532780087, -119499263663, 414431066955, -1440182574644, 5014115406096

Offset

0,4

Comments

A110638 is formed from every 2nd term of A083948, which also consists entirely of numbers 1 through 8.

Links

Table of n, a(n) for n=0..27.

Formula

G.f. A(x) satisfies: A(x)^8 (mod 16) = g.f. of A083948.

Example

A(x) = 1 + x - x^2 + 3*x^3 - 6*x^4 + 18*x^5 - 52*x^6 + 156*x^7 +...
A(x)^4 = 1 + 4*x + 2*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 4*x^6 +...
A(x)^8 = 1 + 8*x + 20*x^2 + 24*x^3 + 50*x^4 + 88*x^5 + 116*x^6 +...
A(x)^8 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +...
G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
where G(x) is the g.f. of A083948.

Prog

(PARI) {a(n)=local(d=2, m=8, 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))))^(1/4), n)}

Crossrefs

Cf. A110638, A083948, A112571.

Sequence in context: A148563 A148564 A148565 * A089325 A110593 A049368

Adjacent sequences: A112569 A112570 A112571 * A112573 A112574 A112575

Keyword

sign

Author

Paul D. Hanna, Sep 14 2005

Status

approved