A112571 G.f. A(x) satisfies: A(x)^2 equals the g.f. of A110637, which consists entirely of numbers 1 through 8.

1, 1, 3, -1, -2, 6, 0, -16, 23, 40, -140, 13, 591, -827, -1577, 5887, -500, -27095, 38922, 77859, -295183, 21310, 1428714, -2069421, -4295099, 16345171, -921876, -81760620, 118435457, 253839799, -963510264, 37372170, 4936868645, -7119213992, -15717478733, 59293735690

Offset

0,3

Comments

A110637 is formed from every 4th term of A083948, which also consists entirely of numbers 1 through 8.

Links

Table of n, a(n) for n=0..35.

Formula

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

Example

A(x) = 1 + x + 3*x^2 - x^3 - 2*x^4 + 6*x^5 - 16*x^7 + 23*x^8 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 4*x^3 + 3*x^4 + 2*x^5 + x^6 + 8*x^7 +...
A(x)^8 = 1 + 8*x + 52*x^2 + 216*x^3 + 754*x^4 + 2008*x^5 +...
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=4, 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))))^(1/2), n)}

Crossrefs

Cf. A110637, A083948.

Sequence in context: A048226 A049919 A246432 * A051277 A300908 A080818

Adjacent sequences: A112568 A112569 A112570 * A112572 A112573 A112574

Keyword

sign

Author

Paul D. Hanna, Sep 14 2005

Status

approved